Pounding Dynamic Responses of Sliding Base-Isolated ...downloads.hindawi.com/journals/sv/2017/8594051.pdf · 4 ShockandVibration Liquid Moat wall Structure Figure2:Slidingbase-isolatedconcreterectangularliquid-storage

Research ArticlePounding Dynamic Responses of SlidingBase-Isolated Rectangular Liquid-Storage Structureconsidering Soil-Structure Interactions

Xuansheng Cheng12 Wei Jing12 Jia Chen12 and Xiaoyan Zhang12

1Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province Lanzhou University of TechnologyLanzhou 730050 China2Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of EducationLanzhou University of Technology Lanzhou 730050 China

Correspondence should be addressed to Xuansheng Cheng chengxuanshenggmailcom and Wei Jing jingwei3276163com

Received 18 August 2016 Revised 19 December 2016 Accepted 4 January 2017 Published 31 January 2017

Academic Editor Ivo Calio

Copyright copy 2017 Xuansheng Cheng et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The soil-structure interaction (SSI) is simulated by an artificial boundary the pounding that occurs between the sliding base-isolatedrectangular liquid-storage structure (LSS) and the surrounding moat wall is considered the instantaneous pounding is simulatedusing the Hertz-damp model and a simplified mechanical model with two particles and four degrees of freedom is establishedDynamic equation is obtained usingHamilton principle effects of SSI initial gap and friction coefficient on the pounding responsesunder the action of near-field pulse-like Chi-Chi earthquake and far-field Imperial Valley-06 earthquake are studied The resultsshow that SSI will amplify liquid sloshing height but that structural acceleration and impact force will be reduced because of SSIThe responses caused by Chi-Chi earthquake are far greater than those of Imperial Valley-06 earthquake Initial gap has a smalleffect on liquid sloshing height structural acceleration and impact force first increase as the initial gap increases and then beginto decrease in the design of moat wall of sliding isolation LSS a certain gap exists that will more adversely affect the poundingresponses of structure Liquid sloshing height is less affected by coefficient of friction but structural acceleration and impact forcedecrease as friction coefficient increases in general

1 Introduction

In lifeline engineering liquid-storage structures play irre-placeable roles in the development of a national economy butmany earthquakes have caused different degrees of damageto the liquid-storage structures Because of the uniqueness ofthis type of structure failure causes some types of disastersuch as a fluid leakage fire or environment pollution Aneffective means to improve the seismic capacity for thisstructure is a special base isolation structure that has beenused widely One of the main shock absorption measures isrubber isolation which can reduce dynamic responses suchas base shear overturningmoment andwall internal force ofthe liquid-storage structure but its effect on liquid sloshingis very limited and may even produce the opposite effect

[1ndash4] However some new types of sliding isolation methodscan achieve independence of the isolation period and liquidsloshing period [5] and avoid the resonance phenomenonwhich can reduce both the structural dynamic responsesand liquid sloshing simultaneously [6 7] Therefore if thisdesign is reasonable the effect of this sliding base-isolatedtechnology will be better than rubber base isolation [8 9]

Although the sliding isolation measure can effectivelyreduce the structure dynamic responses one characteristicof a sliding isolation structure is that it will suffer a largehorizontal displacement during an earthquake For normaluse and structural safety it is very necessary to use acorresponding limiting displacement method At present acommon method the moat wall is widely used in varioustypes of base-isolated structures Although the moat wall

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2 Shock and Vibration

can control the base-isolated structure displacement [10]the pounding between the isolation structure and moat wallgreatly affects the system dynamic responses In recent yearssome scholars have paid attention to the pounding problemofthe base-isolated structure caused by an earthquake and haveachieved certain results Nagarajaiah and Sun [11] assessedthe dynamic responses of a base-isolated structure used for afire control command which was destroyed because of struc-ture and moat wall pounding during the 1994 Northridgeearthquake The results showed that the pounding increasedthe base-isolated structure dynamic responses Matsagar andJangid [12] assumed that pounding occurred only betweenthe bottom of the structure and the moat wall and studiedthe pounding dynamic responses of a building with variousisolation systems Komodromos [13] concluded that thedynamic responses caused by pounding increased as theimpact stiffness and isolation system stiffness increased basedon numerical simulations Fu et al [14] determined thatthe dynamic responses caused by pounding could changethe basic mode of the base-isolated structure and excite ahigher mode of the structure Masroor and Mosqueda [15]considered themoatwall flexibility in a poundingmodel of anisolated structure and found that themoatwall characteristicsgreatly influenced the amplification of the dynamic responseand degree of damage Pant and Wijeyewickrema [16] con-sidered different earthquake excitations and found that thepounding effect had a significant effect on the performance ofan isolated structure Fan et al [17] studied the vulnerabilityof an isolation structure with a moat wall and determinedthat the structure mass and mechanical parameters of anisolation bearing had a greater effect on the maximum basedisplacement Khatiwada and Chouw [18] noted that theimpact stiffness and coefficient of restitution were the mainfactors influencing the pounding responses

The foundation effect is not considered in the abovestudies when the base-isolated structure collides with themoat wall but the SSI has a significant effect on the vibra-tional frequency [19] the systemdamping ratio and rotationaldisplacement of the foundation [20] the structural dynamicresponses [21] and the reasonable choice of the isolationbearing [22] of an isolation structure Currently studies ofthe SSI on the pounding dynamic responses of a structure arevery limited [23] Chau et al [24] noted that the vibrationalresponse of the structure could be amplified but that the SSIcould suppress the vibrational response caused by poundingMahmoud and Gutub [25] found that the SSI effect had amore significant effect on isolated buildings located on a softsoil and the SSI effect could increase the number of collisionsbetween the structure and surrounding moat wall Shakyaand Wijeyewickrema [26] used the gap element and Kelvin-Voigt model to simulate the pounding problem and foundthat the dynamic responses of the structure will be reducedwhen the foundation is considered

In summary the effect of the SSI on the structuraldynamic responses is obvious Although the probability ofpounding of the sliding base-isolated structure with themoat wall is larger than the rubber isolation studies onthe dynamic responses of a sliding isolation structure thatconsider the SSI have not been performed The spring-mass

model is used to simulate the coupling problem of the slidingbase-isolated liquid-storage structure and the 2D viscoelasticartificial boundary is used to simulate the foundation effect Asimplifiedmechanicalmodel and the corresponding dynamicequations of the sliding isolation rectangular liquid-storagestructure that consider the SSI and pounding are estab-lished and the dynamic responses of the rectangular liquid-storage structure experiencing near-field pulse-like Chi-Chiearthquake and far-field Imperial Valley-06 earthquake arestudied Sliding isolation has a certain advantage in theshock absorption of a liquid-storage structure and theoreticalresearch on this type of damping method is helpful to itsfuture application

2 Calculation Model

21 Foundation Model To consider the foundation effectthe lumped parameter model is used to simulate the elasticfoundation and the discrete model which is based on thetheory of a homogeneous isotropic and elastic half spaceTranslation and rotation of the foundation are simulatedusing the spring element and damping element respectivelyand the corresponding parameters can be calculated by usingthe following equations [27]

119896ℎ = 2 (1 minus ]) 119866120573119909radic119861119871119888ℎ = 0576119896ℎ119903ℎradic 120588119866119896119903 = 1198661 minus ]

1205731205931198611198712119888119903 = 031 + 120573120593 119896119903119903119903radic

120588119866

(1)

where ] is Poissonrsquos ratio 119866 is the shear modulus and 120573119909 and120573120593 are the constants to correct the translation and rotation ofthe spring respectively 120573119909 and 120573120593 have strong relationshipswith the foundation length-width ratio and according to theexisting literature [27] the approximate values of 120573119909 and 120573120593are equal to 1 119871 and 119861 are the foundation length and widthrespectively and 119871 and119861 are parallel and perpendicular to thedirection of earthquake respectively 120588 is soil density and 119903ℎand 119903119903 are equivalent radii of the foundation that correspondto translation and rotation respectivelyThemaximum shearmodulus119866max is only suitablewhen the soil is in the low straincondition and it can be expressed as a function of the shearwave velocity 119881119904 and soil density 120588

119866max = 120588 (119881119904)2 (2)

When the soil is in the inelastic stage the shear modulus119866 is significantly reduced The shear modulus 119866 will bechanged when the shear strain 120574 is beyond the range ofthe elastic state because of a dynamic effect To realisticallysimulate the ground effect the shear modulus 119866 needs to bereduced by introducing the shear modulus reduction curve

Shock and Vibration 3

(119866119866max minus 1) [27] and the shear strain 120574 can be expressedas

120574 = 1198814 ( 2120587)05 ( 34119903261198812119904 120588)

sdot [0061 + (0181199038 ) + 03026] + 1198724 ( 2120587)05

sdot ( 1384011990311990332119903261198812119904 120588) (3)

where 119881 is the horizontal shear force and119872 is the overturn-ing moment

22 Pounding Calculation Model Sliding base-isolatedliquid-storage structures will suffer large amounts ofslippage under the action of some strong earthquakesThus the pounding dynamic responses caused by poundingbetween the liquid-storage structure and moat wall areimportant subjects to study The contact element methodis an effective technique to simulate pounding problemscommon pounding models include the linear model Kelvinmodel Hertz model and Hertz-damp model [24 28ndash31]Muthumar and Desroches [29] concluded that for thesame parameters the differences in the displacements andacceleration calculated by the different models are within12 Chau et al [24] and Jankowski [31] systematicallycompared the numerical and experimental results of thepounding models for different materials and showed thatboth the linear and nonlinear pounding models could satisfythe precision requirements for engineering

Previous experimental studies have shown that the energyloss during the pounding process is mainly concentratedwhen the two objects are approaching each other but isrelatively small during the recovery phase [32] The modifiedHertz model (Hertz-damp model) which is composed ofnonlinear springs and a nonlinear damping element (Fig-ure 1) is chosen to simulate the pounding The model doesnot consider the energy loss in the pounding recovery phaseand assumes that all of the energy loss caused by poundingoccurs as the two objects approach each other [31] Thecontact forces during the pounding and recovery phases canbe expressed as (4) and (5) respectively

The pounding occurs on the left

119865119901 = minus119896imp (minus119906119887 minus 119892119901)32 minus 119888imp119887minus119906119887 minus 119892119901 gt 0 119887 lt 0

119865119901 = minus119896imp (minus119906119887 minus 119892119901)32 minus 119906119887 minus 119892119901 gt 0 119887 gt 0119865119901 = 0 minus 119906119887 minus 119892119901 le 0

(4)

kimp

gp

ub

Fp

Figure 1 Hertz-damp pounding model

The pounding occurs on the right

119865119901 = 119896imp (119906119887 minus 119892119901)32 + 119888imp119887 119906119887 minus 119892119901 gt 0 119887 gt 0119865119901 = 119896imp (119906119887 minus 119892119901)32 119906119887 minus 119892119901 gt 0 119887 lt 0119865119901 = 0 119906119887 minus 119892119901 le 0

(5)

where 119906119887 is the horizontal displacement of the liquid-storagestructure 119892119901 is the initial gap between the structure andsurroundingmoat wall or restraining wall 119887 is the structuralvelocity 119896imp is the impact stiffness and 119888imp is the poundingdampingThe parameters 119896imp and 119888imp can be obtained from(6)ndash(9) [29]

119896imp = 43120587 ( 11205821 + 1205822)radic119877111987721198771 + 1198772

120582119894 = 1 minus ]2119894120587119864119894 (119894 = 1 2)119877119894 = 3radic 31198981198944120587120588119894 (119894 = 1 2)

(6)

where 1205821 and 1205822 are the material parameters ]119894 and 119864119894 arePoissonrsquos ratio and elastic modulus of the pounding bodyrespectively119877119894 is the equivalent radius of the pounding bodyand119898119894 and 120588119894 are the mass and density of the pounding bodyrespectively


119888imp = 2120585impradic119896impradic(minus119906119887 minus 119892119901) (119898119888 + 119898119894 + 1198980 + 119898) (7)


119888imp = 2120585impradic119896impradic(119906119887 minus 119892119901) (119898119888 + 119898119894 + 1198980 + 119898) (8)

where 120585imp is the impact damping ratio which can beexpressed as a function of the coefficient of restitution (COR)[33]

120585imp = 9radic52 1 minus COR2

COR (COR (9120587 minus 16) + 16) (9)


Liquid Moat wall

Structure

Figure 2 Sliding base-isolated concrete rectangular liquid-storagestructure with moat wall

After two objects collide with each other the reasonableCOR greatly influences the rationality of the model For mostpounding problems of engineering structures the range ofCORs is 05ndash075 [31]

23 SimplifiedModel of a Sliding Isolation Rectangular Liquid-Storage Structure considering the SSI and Pounding Whenthe sliding base-isolated liquid-storage structure with moatwall (Figure 2) experiences a large earthquake and its mag-nitude of slippage exceeds the initial gap the structure willcollidewith themoatwall To study the influence of poundingon the dynamic responses of the liquid-storage structure areasonable calculationmodel should be developed Currentlythe spring-mass model is generally used as a simplificationof the liquid-storage structure and the structural dynamicresponses are generally calculated accurately [34] In thispaper the liquid is represented using a two-particle model[35] The liquid is divided into 2 parts rigid mass 1198980 andconvective mass 119898119888 In addition the mass of the reinforcedconcrete structure119898 is large so119898 should also be consideredin the dynamic analysis Because of the assumption that 1198980moves with the liquid-storage structure we can add 119898 and1198980 to obtain the total rigid mass 119898 + 1198980 to simplify themodel and reduce the degrees of freedom and the equivalentheights of the two particles are ℎ119888 and ℎ0 respectively Theconvective mass119898119888 is connected to the wall by an equivalentspring with corresponding stiffness and damping of 119896119888 and119888119888 respectively the stiffness and damping of the isolationlayer are 1198960 and 1198880 respectivelyThe lumpedparametermodelwhich is based on the theory of a homogeneous isotropicand elastic half space is used for the massless foundationand the foundation effect is simulated using a 2D viscoelasticartificial boundary The horizontal impedance values of thefoundation are 119896ℎ and 119888ℎ and the rocking impedance valuesof the foundation are 119896120593 and 119888120593

It is assumed that the liquid-storage structure may collidewith both sides of the moat wall during the action of ahorizontal earthquake and the Hertz-damp model is usedto simulate the nonlinear pounding problem The simplified

mechanical model of the sliding base-isolated rectangularliquid-storage structure considering the SSI and pounding isshown in Figure 3

The foundation parameters of the simplified model canbe obtained by (1) and the other system parameters can beobtained by using [36]

119898119888 = 0264 ( 119897ℎ119908) tanh [316 (ℎ119908119897 )]1198721198711198980 = tanh [0866 (119897ℎ119908)]0866 (119897ℎ119908) 119872119871ℎ119888 = 1 minus cosh [316 (ℎ119908119897) minus 1]316 (ℎ119908119897) sinh [316 (ℎ119908119897)] ℎ119908ℎ0 = [05 minus 009375 ( 119897ℎ119908)]

119897ℎ119908 lt 1333ℎ0 = 0375 119897ℎ119908 ge 13331198960 = (2120587119879119887 ) (1198980 + 119898) 1198880 = 2(2120587119879119887 ) 1205850 (1198980 + 119898)

120596119888 = radic119892119899120587119897 tanh(119899120587ℎ119908119897 )119896119888 = 1205962119888119898119888119888119888 = 2120585119888radic119896119888119898119888

(10)

where 119897 is length of the liquid-storage structure which isparallel to the direction of the earthquake action ℎ119908 is theliquid height 119872119871 is the total mass of the liquid 119879119887 is theisolation period 119892 is the acceleration of gravity and 120596119888 iscircular frequency of liquid sloshing

24 Dynamic Equation The dynamic equation of the systemshown in Figure 3 can be obtained using the Hamiltonprinciple

120575int11990521199051

(119879 minus 119881) 119889119905 + int11990521199051

120575119882119899119888119889119905 = 0 (11)

where 119879 and119881 are the kinetic energy and potential energy ofthe system respectively and119882119899119888 is the total energy dissipatedby damping friction and pounding

As seen from Figure 3

119879 = 12119898119888 (119892 + 119891 + 0 + 119888 + ℎ119888)2+ 12 (1198980 + 119898) (119892 + 119891 + 0 + ℎ0)2+ 121198680 ()2


kimp kimpgp gp

uc

ℎc

ℎ0

cimp cimp

120583

c0

k0

m0 + m

mc

cc2

kc2

k0

kℎ kr

uf

cr

u0(t)

cc2

u0

ug(t)

c0

120583

cℎ

kc2

120593

Figure 3 Simplified model of a sliding isolation rectangular liquid-storage structure that considers the SSI and pounding

119881 = 121198961198881199062119888 + 12119896011990620 + 12119896ℎ1199062119891 + 121198961205931205932120575119882119899119888 = minus119888119888119888120575119906119888 minus 119888001205751199060 minus 119888ℎ119891120575119906119891 minus 119888120593120575120593

minus 1198651198911205751199060 minus 1198651199011205751199060(12)

where 119906119891 and 120593 are the horizontal displacement and rotationangle of foundation respectively 1198680 is the structural momentof inertia for rotation around the central axis 119892 119891 0 and119888 are the velocity of the earthquake foundation rigid massand liquid convective mass respectively is the rotationvelocity of the foundation ℎ119888 and ℎ0 are the heights of thecenter of gravity that correspond to the liquid convectivemass and rigid mass respectively 119906119891 1199060 and 119906119888 are thedisplacements of the foundation rigid mass and liquid con-vective mass respectively 120593 is the rotational displacement ofthe foundation 119865119891 is the friction force and 119865119891 = minus120583(119872119871 +119898)119892sign(0) 120583 is the friction coefficient of the isolation layerand sign(0) is a sign function when 0 is greater than zerothe function is equal tominus1 when 0 is less than zero it is equalto 1 and when 0 is 0 it is equal to zero

Inserting (12) into (11) the dynamic equation of thesystem can be obtained

MU + CU + KU + F119891 + F119901 = minusM1015840119892 (13)

where

M

= [[[[[[

119898119888 0 119898119888 119898119888ℎ1198880 119898 + 1198980 119898 + 1198980 0119898119888 119898 + 1198980 119898119888 + 119898 + 1198980 119898119888ℎ119888119898119888ℎ119888 0 119898119888ℎ119888 119898119888ℎ2119888 + 119898ℎ20 + 1198980ℎ20 + 1198680

]]]]]]

C = [[[[[[

119888119888 minus119888119888 0 0minus119888119888 119888119888 + 1198880 0 00 0 119888ℎ 00 0 0 119888119903

]]]]]]

K = [[[[[[

119896119888 minus119896119888 0 0minus119896119888 119896119888 + 1198960 0 00 0 119896ℎ 00 0 0 119896119903

]]]]]]

M1015840 = [[[[[[

119898119888119898 + 1198980119898 + 119898119888 + 1198980119898119888ℎ119888

]]]]]]

U =

1198880119891

U =

1198880119891

U =

1199061198881199060119906119891120593

F119891 =

011986511989100


Table 1 Parameters of the foundation

Soil profiletype

Shear wavevelocity119881119904 (ms)

Soil density120588 (kgm3)Poissonrsquosratio]

Modulus ofelasticity119864 (MPa)

Dampingratio120585 ()

Soft soil 150 1900 030 612 5

F119901 =

011986511990100

(14)

The liquid sloshing height is a characteristic dynamicresponse of liquid-storage structures and should be consid-ered in studies of this type of structures it can be solved byusing [37]

ℎ = 0811 sdot 1198972 sdot (119888 + 119892119892 ) (15)

The energy balance equation can be obtained by using(13)

int11990500U119879MU119889119905 + int1199050

0U119879CU119889119905 + int1199050

0UTKU119889119905

+ int11990500F119891U119889119905 + int1199050

0F119901U119889119905 = minusint1199050

0(M1015840119892)119879U119889119905

(16)

The earthquake input energy of the system can beobtained by further equivalent conversion of the right sideof (16)

119864119868 = int11990500119898119888119888 + (119898 + 1198980) 0 + (119898 + 1198980 + 119898119888) 119891

+ 119898119888ℎ119888 119892119889119905 = int11990500119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) minus (119898 + 1198980 + 119898119888) 119892sdot 119892119889119905 = int1199050

0119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) 119892119889119905 minus int11990500(119898 + 1198980

+ 119898119888) 1198922119892119889119905

(17)

For the sliding base-isolated structure the earthquakeinput energy is mainly dissipated by damping friction and

pounding The energies 119864119863 119864119865 and 119864119875 dissipated by damp-ing friction and pounding respectively can be expressed as

119864119863 = int11990500U119879CU119889119905

119864119865 = int11990500F119891U119889119905

119864119875 = int11990500F119901U119889119905

(18)

3 Pounding Dynamic Responses

31 Calculation Parameters of the System The size of therectangular liquid-storage structure is 6m times 6m times 48m theliquid height is 36m the wall thickness is 02m and themoat wall thickness is 02m The damping ratio 1205850 of thestructure and the liquid rigid mass is 005The damping ratio120585119888 corresponding to the liquid convection mass is 0005 Theimpact stiffness 119896119901 is 275 times 109Nm The impact damping120585imp is 035 the COR is 065 [38]

A large number of studies show that a soft soil causesmore significant changes to the structural dynamic responsesTo study the influence of the foundation effect on thedynamic responses of the sliding base-isolated liquid-storagestructure a soft soil site is assumed to be the foundation basedon the Uniform Building Code (UBC2007) The materialparameters of this soft soil are shown in Table 1The dynamicshear modulus 119866 used to consider the foundation effect isassumed to be 60 of the maximum shear modulus 119866maxThe equivalent radii 119903ℎ and 119903119903 corresponding to foundationtranslation and rotation are 4m [39] and 119871 and 119861 of thefoundation are 66m

32 Seismic Waves The near-field pulse-like Chi-Chi earth-quake and far-field Imperial Valley-06 earthquake are chosento conduct time history analyses The seismic waves arefrom the PEER strong earthquake observation database(httppeerberkeleyedusmcat) and information about theseismic waves is shown in Table 2 To study the dynamicresponses of the sliding base-isolated liquid-storage struc-ture the peak ground acceleration (PGA) of the two seismicwaves is adjusted to 10 g and the adjusted acceleration timehistory curves are shown in Figure 4

33 Effect of the SSI on the Dynamic Responses of a SlidingIsolation Liquid-Storage Structure The initial gap is 010mthe friction coefficient is 006 and the other parameters arementioned previously To study the influences of the SSIon the dynamic responses of a liquid-storage structure the


Table 2 Seismic waves

Earthquake Station PGA (g) PGV (cms) PGD (m) Pulse duration 119879119901 (s)Chi-Chi TCU036 013381 1150826 002336 5341ImperialValley-06

WestmorlandFire Sta 007605 424472 000838 mdash

2 4 6 8 100Time (s)

minus10 minus08 minus06 minus04 minus02

00 02 04 06 08 10

Acce

lera

tion

(ms

2 )

(a) Chi-Chi

0 2Time (s)

4 6 8

Acce

lera

tion

(ms

2 )

minus06 minus04 minus02

00 02 04 06 08 10 12

(b) Imperial Valley-06

Figure 4 Seismic waves

structural dynamic responses are calculated with andwithoutthe SSI The liquid sloshing height structural acceleration0 impact force and structural displacement 1199060 for the twoconditions are shown in Figure 5

As shown in Figure 5 the impact force and structuralacceleration show the pulse phenomenon at the momentof pounding The liquid sloshing height increases when theSSI is considered the probable reason being that the SSIeffect extends the period of the isolation system namelythe periods of the system corresponding to considering theSSI and not considering the SSI are 20 s and 23 s besidesthe liquid sloshing period (2726 s) is long Because thedifference of structure period and liquid sloshing periodbecomes small the liquid sloshing height is increased Thestructural acceleration and impact force will be reduced afterconsidering the SSI because the foundation plays the roleof a buffer at the moment of pounding Under the actionof strong near-field Chi-Chi and far-field Imperial Valley-06 earthquake the structural slippage will exceed the initialgap but the sliding of the structure is limited because ofthe action of the surrounding moat wall so the influenceof the SSI effect on the maximum displacement response ofthe structure is relatively small In addition to the slippagethe structural dynamic response induced by the near-fieldearthquake is much larger than the response due to the far-field earthquake After considering the SSI the maximumliquid sloshing heights under the action of near-field and far-field earthquakes are 0822m and 0266m respectively themaximum structural acceleration values are 4936ms2 and1759ms2 respectively and the maximum impact forces are702 times 106N and 170 times 106N respectively From this analysiswe can conclude that near-field pulse-like Chi-Chi earth-quake causes more serious damage to a sliding base-isolatedstructure than far-field Imperial Valley-06 earthquake and

that the former will greatly influence the function of thesliding isolation structure

34 Effect of the SSI on the Energy Responses of a Liquid-Storage Structure A remarkable characteristic of sliding iso-lation is that the friction effect will consume a large amount ofenergy when the structure moves In addition the dampingof the system will dissipate a portion of the energy and thepounding effect can dissipate another portion of the energywhen pounding occurs In addition in order to validatethe motion equations derived from Hamiltonrsquos principle theinput energy of the earthquake and the total dissipated energyconsidering the SSI effect are shown in Figure 6 For the twotypes of earthquake actions the friction energy dissipation119864119865 the pounding energy dissipation 119864119875 and the dampingenergy dissipation 119864119863 that consider the SSI or not are shownin Figure 7

As seen from Figure 6 under the action of Chi-Chiand Imperial Valley-06 earthquakes the difference of inputenergy curve and total dissipated energy curve is smallwhen the SSI effect is considered so the rationality of thecorresponding equations proposed in this paper is verifiedto a certain degree Besides it is shown that the earthquakeinput energy is mainly dissipated by damping friction andpounding

As seen in Figure 7 the friction energy dissipation and thepounding energy dissipation are decreased and the dampingenergy dissipation is increased when the SSI are considered119864119865 and 119864119863 increase gradually as the time increases andfinally they tend to be stable 119864119875 only occurs at everypounding moment For the no pounding state 119864119875 does notincrease and the corresponding curve is linear so 119864119875 hasa ladder-type growth phenomenon with time The frictionenergy dissipation of the sliding isolation structure is much


Without SSIWith SSI

Without SSIWith SSI

Chi-Chi Imperial Valley-06


00 02 04 06 08 10

Liqu

id sl

oshi

ng h

eigh

t (m

)

minus06

minus04

minus02

00

02

04

Liqu

id sl

oshi

ng h

eigh

t (m

)

2 4 6 80Time (s)

2 4 6 8 100Time (s)

(a) Liquid sloshing height

Without SSIWith SSI

Without SSIWith SSI


Acce

lera

tion

(ms

2 )

Acce

lera

tion

(ms

2 )

minus600

minus400

minus200

00

200

400

600


minus50 00 50

100 150 200

2 4 6 8 100Time (s)

2 4 6 80Time (s)

(b) Structural acceleration

Without SSIWith SSI

Without SSIWith SSI


0 2Time (s)

4 6 8minus8 minus6 minus4 minus2

0 2 4 6 8

Impa

ct fo

rce (

N)


00 05 10 15 20 25

Impa

ct fo

rce (

N)

times106times106

2 4 6 8 100Time (s)

(c) Impact force

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

2 4 6 80Time (s)

(d) Structural displacement

Figure 5 Effect of SSI on structural dynamic responses considering pounding


0

1

2

3

4

0 2 4 6 8 10Time (s)

Input energyTotal dissipated energy

Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)


Imperial Valley-06En

ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104

Figure 6 Comparison of input energy and total dissipated energy

larger than the damping energy dissipation Therefore areasonable selection of the friction coefficient of the slidingisolation layer has an important influence on the design ofthe sliding isolation structure

By comparing the corresponding energy responses forthe actions of the near-field pulse-like Chi-Chi earthquakeand far-field Imperial Valley-06 earthquake we found that119864119865 119864119875 and 119864119863 corresponding to the Chi-Chi wave aremuch larger than those of the Imperial Valley-06 wave Toensure that a sliding base-isolated liquid-storage structurethat experiences strong earthquakes can continue to play itsimportant role the design requirements of each part of thestructure should be higher for near-field pulse-like Chi-Chiearthquake because each part of the system needs to dissipatemore seismic energy

4 Peak Response Analysis

41 Effect of the Initial Gap on Peak Responses 119892119901 is oneof the important parameters in the design of base-isolatedstructures and the gap size determines the occurrence ofpounding and the impact of pounding on the structuraldynamic responses To study the influence of 119892119901 on thedynamic responses while considering the SSI of a slidingisolation rectangular liquid-storage structure different valuesof 119892119901 liquid sloshing height structural acceleration andimpact force corresponding to different 119892119901 are studied Thecalculated results are shown in Figure 8

As shown in Figure 8 119892119901 has little effect on the liquidsloshing height after considering the SSI The maximum liq-uid sloshing height caused by near-field Chi-Chi earthquakeis approximately 2-3 times the height of the far-field ImperialValley-06 earthquake for a given value of 119892119901 In additionto some individual 119892119901 the response of the impact forceand structural acceleration caused by the near-field Chi-Chiearthquake is much larger than the far-field Imperial Valley-06 earthquake overall and the impact force and structuralacceleration first increase and then decrease as 119892119901 increasesFor the Chi-Chi and Imperial Valley-06 waves the structuralacceleration and impact forces are maximum values when 119892119901is 004m and 018m respectively Therefore in the design

of a sliding isolation structure there is critical 119892119901 that willcause the maximum dynamic responses when the pound-ing occurs which makes the structure more susceptible todamage and seriously affects the effectiveness of the isolationstructure Moreover 119892119901 corresponding to near-field Chi-Chiearthquake and far-field Imperial Valley-06 earthquake thathave more adverse effects on the structure is different In thedesign of this type of structure to select a reasonable gap tominimize the adverse effect of pounding on the system thesite conditions should be seriously considered

42 Effect of the Friction Coefficient on the Peak ResponsesFriction coefficient 120583 is an important design parameter of asliding isolation structure because it directly determines theshock absorption effect of this type of structure For the casethat considers the foundation effect studying the influenceof 120583 on the dynamic responses is helpful to understand thepounding of the sliding isolation structure and to provide atheoretical basis for a rational design of a sliding isolationstructure After the SSI is considered the liquid sloshingheight structural acceleration and impact force correspond-ing to different friction coefficients are shown in Figure 9

As seen in Figure 9 the friction coefficient has little effecton the liquid sloshing wave height for the case of poundingthat considers the SSI In addition to the friction coefficientsof 008 and 010 the impact force and structural accelera-tion decrease as the friction coefficient increases overall Incomparison based on fitted curve we obtained the influenceof the friction coefficient on the dynamic response of thestructure for the near-field Chi-Chi earthquake is less thanthe far-field Imperial Valley-06 earthquake However underdifferent friction coefficients the dynamic responses of thesystem for the near-field Chi-Chi earthquake are significantlygreater than the far-field Imperial Valley-06 earthquake Thelarger coefficient of friction can reduce the probability ofpounding and the structural dynamic responses in the caseof pounding However it should be noted that the effect ofthis type of base-isolated structure is achieved by slidingWhen the friction coefficient is too large the structure willnot slip under some smaller earthquakes which is similar tothe structure with a fixed support so that the damping effect


Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104

(a) Friction energy dissipation 119864119865

Without SSIWith SSI

Without SSIWith SSI

Chi-Chi Imperial Valley-06EP

(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104

(b) Pounding energy dissipation 119864119875

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104

(c) Damping energy dissipation 119864119863

Figure 7 Effects of SSI on energy dissipation

of the sliding isolation structure will be lost Therefore aftercomprehensive consideration the friction coefficient shouldbe an intermediate value to better balance the needs of allparties

43 Correlation of the Friction Coefficient and Initial Gapon the Maximum Horizontal Displacement of the StructureSlippage is an important characteristic dynamic response of asliding isolation structure Although the amount of slippagehas little effect on the liquid-storage structure in theory

when taking into account some practical problems especiallyliquid-storage structures in the petroleum chemical industryand nuclear industry once the slippage exceeds a criticallimit the accessory pipelines will be damaged and liquidmayleak out This result is as serious as failure of the structureitself If we ignore the problem the loss of a sliding isolationstructure will outweigh the gain To have a more compre-hensive understanding of the slippage of the sliding isolationstructure the correlation effect of the friction coefficient andinitial gap on the maximum horizontal displacement of a


Chi-ChiImperial Valley-06

00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force

Figure 8 Pounding dynamic responses corresponding to different gap sizes

00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force

Figure 9 Pounding dynamic responses corresponding to different friction coefficients


008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)

Friction coefficient

01000

01150

01300

01450

01600

01750

01900

02050

02200

(a) Chi-Chi earthquake

008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200

(b) Imperial Valley-06 earthquake

Figure 10 Correlation effects of the friction coefficient and initial gap on the maximum horizontal displacement of the structure

liquid-storage structure is studied considering the SSI Thecalculated results are shown in Figure 10

As seen in Figure 10 the maximum horizontal displace-ment of the liquid-storage structure decreases as the frictioncoefficient increases and increases as the initial gap increasesoverall Under the near-field Chi-Chi earthquake when theinitial gap 119892119901 is small (010m and 012m) the frictioncoefficient has little effect on the maximum slippage of theliquid-storage structure because the maximum horizontaldisplacement of the liquid-storage structure with differentfriction coefficients can all reach119892119901 As119892119901 increases the effectof the friction coefficient on the slippage becomes obviousIn particular when 119892119901 is greater than or equal to 020 as thefriction coefficient increases the decreasing trend of slippageis evenmore significantWhen the friction coefficient is largethe slippage is small so 119892119901 has little effect on the slippageFor the far-field Imperial Valley-06 earthquake when thefriction coefficient is small (such as 008 or 010) the slippageincreases with increase of 119892119901 When the friction coefficientis greater than or equal to 012 the structure will not collidewith the moat wall so 119892119901 has no effect on the slippage

Based on the calculated results of Figure 10 if there isno surrounding moat wall the maximum slippage will begreater than 020m for the near-field Chi-Chi earthquakeand the maximum slippage will be smaller than 012m forthe far-field Imperial Valley-06 earthquake Therefore theamount of slippage for the structure experiencing near-fieldChi-Chi earthquake is significantly greater than the far-fieldImperial Valley-06 earthquake To avoid damage caused bylarge amounts of slippage to accessory pipelines of a slidingliquid-storage structure in the petroleum chemical industrya study of limiting measures for near-field pulse-like earth-quakes should receive great attention Meanwhile for near-field pulse-like Chi-Chi earthquake it is more necessary tostudy mitigation measures to reduce the pounding dynamicresponses

5 Conclusions

The SSI and the pounding possibility between a sliding isola-tion liquid-storage structure and its moat wall are considered

in this paper A simplified mechanical model of the slidingbase-isolated liquid-storage structure is established and thepounding dynamic responses of the system under the actionnear-field Chi-Chi earthquake and far-field Imperial Valley-06 earthquake are studied The effects of the SSI initial gapand friction coefficient on the dynamic responses of a liquid-storage structure are discussed The main conclusions are asfollows

(1) The liquid sloshing height of a sliding isolation liquid-storage structure increases when the SSI is consideredbecause the SSI increases the period of the isolationstructure and the difference between the isolationperiod and liquid sloshing period becomes smallWhen the liquid-storage structure collides with themoat wall the structural dynamic responses due toa pulse phenomenon will appear but the structuralacceleration and impact force are reduced because ofthe buffer effect of the foundation

(2) The friction energy dissipation and pounding energydissipation of the system are reduced when the SSIis considered The friction energy dissipation anddamping energy dissipation gradually increase asthe time increases whereas the pounding energydissipation is only affected by each pounding andshows a ladder-type growth phenomenon as the timeincreases The friction energy dissipation poundingenergy dissipation and damping energy dissipationfor near-field pulse-like Chi-Chi earthquake are fargreater than far-field Imperial Valley-06 earthquakeTo ensure that the structure continues to workproperly under some strong earthquakes the near-field pulse-like Chi-Chi earthquake affects the designprocess more for each part of the structure

(3) After considering the SSI the dynamic responses ofa sliding isolation liquid-storage structure with dif-ferent initial gaps for near-field Chi-Chi earthquakeare generally larger than far-field Imperial Valley-06earthquake 119892119901 has little effect on the liquid sloshingheight but the structural acceleration and impact


force first increase and then decrease as 119892119901 increasesTherefore when designing a sliding isolation struc-ture it should be noted that a certain value of 119892119901 willresult in the maximum pounding dynamic responsesand the effectiveness of the isolation structure will beseriously affected

(4) Increasing the friction coefficient can reduce thepounding dynamic responses of the structure to acertain extent However when the friction coefficientis large this type of isolation structure will not slideso it will lose the designed shock absorption duringsome earthquakesTherefore the selection of the fric-tion coefficient of a sliding isolation structure shouldbe considered comprehensively and an intermediatevalue for the friction coefficient is ideal

(5) When the friction coefficient is small the initial gapgreatly affects the slippage of a sliding isolation liquid-storage structure When the initial gap is large thefriction coefficient greatly affects the slippage of thesliding isolation liquid-storage structure

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This paper is supported in part by the National NaturalScience Foundation of China (Grant nos 51368039 and51478212) the Education Ministry Doctoral Tutor Founda-tion of China (Grant no 20136201110003) and the PlanProject of Science and Technology in Gansu Province (Grantno 144GKCA032)

References

[1] M R Shekari N Khaji and M T Ahmadi ldquoA coupled BE-FE study for evaluation of seismically isolated cylindrical liquidstorage tanks considering fluid-structure interactionrdquo Journal ofFluids amp Structures vol 25 no 3 pp 567ndash585 2009

[2] H Vosoughifar andMNaderi ldquoNumerical analysis of the base-isolated rectangular storage tanks under bi-directional seismicexcitationrdquo British Journal of Mathematics amp Computer Sciencevol 4 no 21 pp 3054ndash3067 2014

[3] X Cheng L Cao andH Zhu ldquoLiquid-solid interaction seismicresponse of an isolated overground rectangular reinforced-concrete liquid-storage structurerdquo Journal of Asian Architectureand Building Engineering vol 14 no 1 pp 175ndash180 2015

[4] X S Cheng L Zhao Y R Zhao and A J Zhang ldquoFSIresonance response of liquid-storage structuresmade of rubber-isolated rectangular reinforced concreterdquo Electronic Journal ofGeotechnical Engineering vol 20 no 7 pp 1809ndash1824 2015

[5] E Abali and E Uckan ldquoParametric analysis of liquid storagetanks base isolated by curved surface sliding bearingsrdquo SoilDynamics amp Earthquake Engineering vol 30 no 1-2 pp 21ndash312010

[6] R Zhang D Weng and X Ren ldquoSeismic analysis of a LNGstorage tank isolated by a multiple friction pendulum systemrdquo

Earthquake Engineering and Engineering Vibration vol 10 no2 pp 253ndash262 2011

[7] V R Panchal and R S Jangid ldquoSeismic response of liquidstorage steel tanks with variable frequency pendulum isolatorrdquoKSCE Journal of Civil Engineering vol 15 no 6 pp 1041ndash10552011

[8] M K Shrimali and R S Jangid ldquoA comparative study ofperformance of various isolation systems for liquid storagetanksrdquo International Journal of Structural Stability amp Dynamicsvol 2 no 4 pp 573ndash591 2002

[9] A A Seleemah and M El-Sharkawy ldquoSeismic response of baseisolated liquid storage ground tanksrdquo Ain Shams EngineeringJournal vol 2 no 1 pp 33ndash42 2011

[10] J Liu SWang Y Shi andX Cao ldquoShaking table test for isolatedstructures supported on slide-limited innovative separated fric-tion sliding devicerdquo Xirsquoan Jianzhu Keji Daxue XuebaoJournal ofXirsquoan University of Architecture and Technology vol 47 no 4 pp498ndash502 2015

[11] S Nagarajaiah and X Sun ldquoBase-isolated FCC building impactresponse in Northridge earthquakerdquo Journal of Structural Engi-neering vol 127 no 9 pp 1063ndash1075 2001

[12] V A Matsagar and R S Jangid ldquoSeismic response of base-isolated structures during impact with adjacent structuresrdquoEngineering Structures vol 25 no 10 pp 1311ndash1323 2003

[13] P Komodromos ldquoSimulation of the earthquake-inducedpounding of seismically isolated buildingsrdquo Computers andStructures vol 86 no 7-8 pp 618ndash626 2008

[14] R Fu K Ye and L Li ldquoSeismic response of LRB base-isolated structures under near-fault pulse-like ground motionsconsidering potential poundingrdquo Engineering Mechanics vol27 no 2 pp 298ndash302 2010

[15] A Masroor and G Mosqueda ldquoImpact model for simulationof base isolated buildings impacting flexible moat wallsrdquo Earth-quake EngineeringampStructuralDynamics vol 42 no 3 pp 357ndash376 2013

[16] D R Pant and A C Wijeyewickrema ldquoPerformance ofbase-isolated reinforced concrete buildings under bidirectionalseismic excitation considering pounding with retaining wallsincluding friction effectsrdquo Earthquake Engineering and Struc-tural Dynamics vol 43 no 10 pp 1521ndash1541 2014

[17] J Fan X-H Long and J Zhao ldquoCaculation on robust fragilitycurves of base-isolated structure under near-fault earthquakeconsidering base poundingrdquo Engineering Mechanics vol 31 no1 pp 166ndash172 2014

[18] S Khatiwada and N Chouw ldquoLimitations in simulation ofbuilding pounding in earthquakesrdquo International Journal ofProtective Structures vol 5 no 2 pp 123ndash150 2014

[19] W Q Liu C-P Li S G Wang D S Du and H WangldquoComparative study on high-rise isolated structure founded onvarious soil foundations by using shaking table testsrdquo Zhendongyu ChongjiJournal of Vibration and Shock vol 32 no 16 pp128ndash151 2013

[20] Z Haiyang Y Xu Z Chao and J Dandan ldquoShaking table testsfor the seismic response of a base-isolated structure with theSSI effectrdquo Soil Dynamics amp Earthquake Engineering vol 67 pp208ndash218 2014

[21] A Krishnamoorthy and S Anita ldquoSoil-structure interactionanalysis of a FPS-isolated structure using finite element modelrdquoStructures vol 5 pp 44ndash57 2016

[22] T Karabork I O Deneme and R P Bilgehan ldquoA comparisonof the effect of SSI on base isolation systems and fixed-base


structures for soft soilrdquo Geomechanics and Engineering vol 7no 1 pp 87ndash103 2014

[23] P Komodromos P C Polycarpou L Papaloizou and M CPhocas ldquoResponse of seismically isolated buildings consideringpoundingsrdquo Earthquake Engineering amp Structural Dynamicsvol 36 no 12 pp 1605ndash1622 2007

[24] K T Chau X X Wei X Guo and C Y Shen ldquoExperimentaland theoretical simulations of seismic poundings betweentwo adjacent structuresrdquo Earthquake Engineering amp StructuralDynamics vol 32 no 4 pp 537ndash554 2003

[25] S Mahmoud and S A Gutub ldquoEarthquake induced pounding-involved response of base-isolated buildings incorporating soilflexibilityrdquo Advances in Structural Engineering vol 16 no 122013

[26] K Shakya and A C Wijeyewickrema ldquoMid-column poundingof multi-story reinforced concrete buildings considering soileffectsrdquoAdvances in Structural Engineering vol 12 no 1 pp 71ndash85 2009

[27] R V Whitman and F E Richart ldquoDesign procedures fordynamically loaded foundationsrdquo Journal of Soil Mechanics ampFoundations Division ASCE vol 92 no 6 pp 169ndash193 1967

[28] S Mahmoud A Abd-Elhamed and R Jankowski ldquoEarth-quake-induced pounding between equal height multi-storeybuildings considering soil-structure interactionrdquo Bulletin ofEarthquake Engineering vol 11 no 4 pp 1021ndash1048 2013

[29] S Muthukumar and R Desroches ldquoEvaluation of impactmodels for seismic poundingrdquo in Proceedings of the 13th WorldConference on Earthquake Engineering Vancouver Canada2004

[30] S Mahmoud and R Jankowski ldquoModified linear viscoelasticmodel of earthquake-induced structural poundingrdquo IranianJournal of Science amp Technology Transaction B Engineering vol35 no 1 pp 51ndash62 2011

[31] R Jankowski ldquoNon-linear viscoelastic modelling of earth-quake-induced structural poundingrdquo Earthquake Engineeringand Structural Dynamics vol 34 no 6 pp 595ndash611 2005

[32] W Goldsmith Impact The Theory and Physical Behavior ofColliding Solids Edward Arnold London UK 1st edition 1960

[33] R Jankowski ldquoAnalytical expression between the impact damp-ing ratio and the coefficient of restitution in the non-linearviscoelastic model of structural poundingrdquo Earthquake Engi-neering and Structural Dynamics vol 35 no 4 pp 517ndash5242006

[34] Q Z Ge D G Weng and R F Zhang ldquoA nonlinear simplifiedmodel of liquid storage tank and primary resonance analysisrdquoGongcheng LixueEngineering Mechanics vol 31 no 5 pp 166ndash202 2014

[35] GW Housner ldquoThe dynamic behavior of water tanksrdquo Bulletinof the Seismological Society of America vol 53 no 2 pp 381ndash3871963

[36] ACI Committee 350 ldquoSeismic design of liquid-containing con-crete structures (ACI 3503-01) and commentary (ACI 3503R-01)rdquo American Concrete Institute Farmington Hills MissUSA 2001

[37] K Ikago K Saito and N Inoue ldquoSeismic control of single-degree-of-freedom structure using tuned viscousmass damperrdquoEarthquake Engineering amp Structural Dynamics vol 41 no 3pp 453ndash474 2012

[38] R Jankowski ldquoEarthquake-induced pounding between equalheight buildings with substantially different dynamic proper-tiesrdquo Engineering Structures vol 30 no 10 pp 2818ndash2829 2008

[39] I Takewaki ldquoBound of earthquake input energy to soil-structure interaction systemsrdquo Soil Dynamics amp EarthquakeEngineering vol 25 no 7ndash10 pp 741ndash752 2005

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Navigation and Observation



DistributedSensor Networks



can control the base-isolated structure displacement [10]the pounding between the isolation structure and moat wallgreatly affects the system dynamic responses In recent yearssome scholars have paid attention to the pounding problemofthe base-isolated structure caused by an earthquake and haveachieved certain results Nagarajaiah and Sun [11] assessedthe dynamic responses of a base-isolated structure used for afire control command which was destroyed because of struc-ture and moat wall pounding during the 1994 Northridgeearthquake The results showed that the pounding increasedthe base-isolated structure dynamic responses Matsagar andJangid [12] assumed that pounding occurred only betweenthe bottom of the structure and the moat wall and studiedthe pounding dynamic responses of a building with variousisolation systems Komodromos [13] concluded that thedynamic responses caused by pounding increased as theimpact stiffness and isolation system stiffness increased basedon numerical simulations Fu et al [14] determined thatthe dynamic responses caused by pounding could changethe basic mode of the base-isolated structure and excite ahigher mode of the structure Masroor and Mosqueda [15]considered themoatwall flexibility in a poundingmodel of anisolated structure and found that themoatwall characteristicsgreatly influenced the amplification of the dynamic responseand degree of damage Pant and Wijeyewickrema [16] con-sidered different earthquake excitations and found that thepounding effect had a significant effect on the performance ofan isolated structure Fan et al [17] studied the vulnerabilityof an isolation structure with a moat wall and determinedthat the structure mass and mechanical parameters of anisolation bearing had a greater effect on the maximum basedisplacement Khatiwada and Chouw [18] noted that theimpact stiffness and coefficient of restitution were the mainfactors influencing the pounding responses

The foundation effect is not considered in the abovestudies when the base-isolated structure collides with themoat wall but the SSI has a significant effect on the vibra-tional frequency [19] the systemdamping ratio and rotationaldisplacement of the foundation [20] the structural dynamicresponses [21] and the reasonable choice of the isolationbearing [22] of an isolation structure Currently studies ofthe SSI on the pounding dynamic responses of a structure arevery limited [23] Chau et al [24] noted that the vibrationalresponse of the structure could be amplified but that the SSIcould suppress the vibrational response caused by poundingMahmoud and Gutub [25] found that the SSI effect had amore significant effect on isolated buildings located on a softsoil and the SSI effect could increase the number of collisionsbetween the structure and surrounding moat wall Shakyaand Wijeyewickrema [26] used the gap element and Kelvin-Voigt model to simulate the pounding problem and foundthat the dynamic responses of the structure will be reducedwhen the foundation is considered

In summary the effect of the SSI on the structuraldynamic responses is obvious Although the probability ofpounding of the sliding base-isolated structure with themoat wall is larger than the rubber isolation studies onthe dynamic responses of a sliding isolation structure thatconsider the SSI have not been performed The spring-mass

model is used to simulate the coupling problem of the slidingbase-isolated liquid-storage structure and the 2D viscoelasticartificial boundary is used to simulate the foundation effect Asimplifiedmechanicalmodel and the corresponding dynamicequations of the sliding isolation rectangular liquid-storagestructure that consider the SSI and pounding are estab-lished and the dynamic responses of the rectangular liquid-storage structure experiencing near-field pulse-like Chi-Chiearthquake and far-field Imperial Valley-06 earthquake arestudied Sliding isolation has a certain advantage in theshock absorption of a liquid-storage structure and theoreticalresearch on this type of damping method is helpful to itsfuture application

2 Calculation Model

21 Foundation Model To consider the foundation effectthe lumped parameter model is used to simulate the elasticfoundation and the discrete model which is based on thetheory of a homogeneous isotropic and elastic half spaceTranslation and rotation of the foundation are simulatedusing the spring element and damping element respectivelyand the corresponding parameters can be calculated by usingthe following equations [27]

119896ℎ = 2 (1 minus ]) 119866120573119909radic119861119871119888ℎ = 0576119896ℎ119903ℎradic 120588119866119896119903 = 1198661 minus ]

1205731205931198611198712119888119903 = 031 + 120573120593 119896119903119903119903radic

120588119866

(1)

where ] is Poissonrsquos ratio 119866 is the shear modulus and 120573119909 and120573120593 are the constants to correct the translation and rotation ofthe spring respectively 120573119909 and 120573120593 have strong relationshipswith the foundation length-width ratio and according to theexisting literature [27] the approximate values of 120573119909 and 120573120593are equal to 1 119871 and 119861 are the foundation length and widthrespectively and 119871 and119861 are parallel and perpendicular to thedirection of earthquake respectively 120588 is soil density and 119903ℎand 119903119903 are equivalent radii of the foundation that correspondto translation and rotation respectivelyThemaximum shearmodulus119866max is only suitablewhen the soil is in the low straincondition and it can be expressed as a function of the shearwave velocity 119881119904 and soil density 120588

119866max = 120588 (119881119904)2 (2)

When the soil is in the inelastic stage the shear modulus119866 is significantly reduced The shear modulus 119866 will bechanged when the shear strain 120574 is beyond the range ofthe elastic state because of a dynamic effect To realisticallysimulate the ground effect the shear modulus 119866 needs to bereduced by introducing the shear modulus reduction curve



120574 = 1198814 ( 2120587)05 ( 34119903261198812119904 120588)

sdot [0061 + (0181199038 ) + 03026] + 1198724 ( 2120587)05

sdot ( 1384011990311990332119903261198812119904 120588) (3)







(4)

kimp

gp

ub

Fp




(5)


119896imp = 43120587 ( 11205821 + 1205822)radic119877111987721198771 + 1198772

120582119894 = 1 minus ]2119894120587119864119894 (119894 = 1 2)119877119894 = 3radic 31198981198944120587120588119894 (119894 = 1 2)

(6)








COR (COR (9120587 minus 16) + 16) (9)


Liquid Moat wall

Structure








119897ℎ119908 lt 1333ℎ0 = 0375 119897ℎ119908 ge 13331198960 = (2120587119879119887 ) (1198980 + 119898) 1198880 = 2(2120587119879119887 ) 1205850 (1198980 + 119898)


(10)



120575int11990521199051

(119879 minus 119881) 119889119905 + int11990521199051

120575119882119899119888119889119905 = 0 (11)



119879 = 12119898119888 (119892 + 119891 + 0 + 119888 + ℎ119888)2+ 12 (1198980 + 119898) (119892 + 119891 + 0 + ℎ0)2+ 121198680 ()2


kimp kimpgp gp

uc

ℎc

ℎ0

cimp cimp

120583

c0

k0

m0 + m

mc

cc2

kc2

k0

kℎ kr

uf

cr

u0(t)

cc2

u0

ug(t)

c0

120583

cℎ

kc2

120593



minus 1198651198911205751199060 minus 1198651199011205751199060(12)



MU + CU + KU + F119891 + F119901 = minusM1015840119892 (13)

where

M

= [[[[[[

119898119888 0 119898119888 119898119888ℎ1198880 119898 + 1198980 119898 + 1198980 0119898119888 119898 + 1198980 119898119888 + 119898 + 1198980 119898119888ℎ119888119898119888ℎ119888 0 119898119888ℎ119888 119898119888ℎ2119888 + 119898ℎ20 + 1198980ℎ20 + 1198680

]]]]]]

C = [[[[[[

119888119888 minus119888119888 0 0minus119888119888 119888119888 + 1198880 0 00 0 119888ℎ 00 0 0 119888119903

]]]]]]

K = [[[[[[

119896119888 minus119896119888 0 0minus119896119888 119896119888 + 1198960 0 00 0 119896ℎ 00 0 0 119896119903

]]]]]]

M1015840 = [[[[[[

119898119888119898 + 1198980119898 + 119898119888 + 1198980119898119888ℎ119888

]]]]]]

U =

1198880119891

U =

1198880119891

U =

1199061198881199060119906119891120593

F119891 =

011986511989100



Soil profiletype





Soft soil 150 1900 030 612 5

F119901 =

011986511990100

(14)


ℎ = 0811 sdot 1198972 sdot (119888 + 119892119892 ) (15)


int11990500U119879MU119889119905 + int1199050

0U119879CU119889119905 + int1199050

0UTKU119889119905

+ int11990500F119891U119889119905 + int1199050

0F119901U119889119905 = minusint1199050

0(M1015840119892)119879U119889119905

(16)


119864119868 = int11990500119898119888119888 + (119898 + 1198980) 0 + (119898 + 1198980 + 119898119888) 119891

+ 119898119888ℎ119888 119892119889119905 = int11990500119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) minus (119898 + 1198980 + 119898119888) 119892sdot 119892119889119905 = int1199050

0119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) 119892119889119905 minus int11990500(119898 + 1198980

+ 119898119888) 1198922119892119889119905

(17)



119864119863 = int11990500U119879CU119889119905

119864119865 = int11990500F119891U119889119905

119864119875 = int11990500F119901U119889119905

(18)










2 4 6 8 100Time (s)


00 02 04 06 08 10

Acce

lera

tion

(ms

2 )

(a) Chi-Chi

0 2Time (s)

4 6 8

Acce

lera

tion

(ms

2 )


00 02 04 06 08 10 12










Without SSIWith SSI

Without SSIWith SSI



00 02 04 06 08 10

Liqu

id sl

oshi

ng h

eigh

t (m

)

minus06

minus04

minus02

00

02

04

Liqu

id sl

oshi

ng h

eigh

t (m

)

2 4 6 80Time (s)

2 4 6 8 100Time (s)


Without SSIWith SSI

Without SSIWith SSI


Acce

lera

tion

(ms

2 )

Acce

lera

tion

(ms

2 )

minus600

minus400

minus200

00

200

400

600


minus50 00 50

100 150 200

2 4 6 8 100Time (s)

2 4 6 80Time (s)


Without SSIWith SSI

Without SSIWith SSI


0 2Time (s)


0 2 4 6 8

Impa

ct fo

rce (

N)


00 05 10 15 20 25

Impa

ct fo

rce (

N)

times106times106

2 4 6 8 100Time (s)

(c) Impact force

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

2 4 6 80Time (s)




0

1

2

3

4

0 2 4 6 8 10Time (s)


Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)



ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104











Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120574 = 1198814 ( 2120587)05 ( 34119903261198812119904 120588)

sdot [0061 + (0181199038 ) + 03026] + 1198724 ( 2120587)05

sdot ( 1384011990311990332119903261198812119904 120588) (3)







(4)

kimp

gp

ub

Fp




(5)


119896imp = 43120587 ( 11205821 + 1205822)radic119877111987721198771 + 1198772

120582119894 = 1 minus ]2119894120587119864119894 (119894 = 1 2)119877119894 = 3radic 31198981198944120587120588119894 (119894 = 1 2)

(6)








COR (COR (9120587 minus 16) + 16) (9)


Liquid Moat wall

Structure








119897ℎ119908 lt 1333ℎ0 = 0375 119897ℎ119908 ge 13331198960 = (2120587119879119887 ) (1198980 + 119898) 1198880 = 2(2120587119879119887 ) 1205850 (1198980 + 119898)


(10)



120575int11990521199051

(119879 minus 119881) 119889119905 + int11990521199051

120575119882119899119888119889119905 = 0 (11)



119879 = 12119898119888 (119892 + 119891 + 0 + 119888 + ℎ119888)2+ 12 (1198980 + 119898) (119892 + 119891 + 0 + ℎ0)2+ 121198680 ()2


kimp kimpgp gp

uc

ℎc

ℎ0

cimp cimp

120583

c0

k0

m0 + m

mc

cc2

kc2

k0

kℎ kr

uf

cr

u0(t)

cc2

u0

ug(t)

c0

120583

cℎ

kc2

120593



minus 1198651198911205751199060 minus 1198651199011205751199060(12)



MU + CU + KU + F119891 + F119901 = minusM1015840119892 (13)

where

M

= [[[[[[

119898119888 0 119898119888 119898119888ℎ1198880 119898 + 1198980 119898 + 1198980 0119898119888 119898 + 1198980 119898119888 + 119898 + 1198980 119898119888ℎ119888119898119888ℎ119888 0 119898119888ℎ119888 119898119888ℎ2119888 + 119898ℎ20 + 1198980ℎ20 + 1198680

]]]]]]

C = [[[[[[

119888119888 minus119888119888 0 0minus119888119888 119888119888 + 1198880 0 00 0 119888ℎ 00 0 0 119888119903

]]]]]]

K = [[[[[[

119896119888 minus119896119888 0 0minus119896119888 119896119888 + 1198960 0 00 0 119896ℎ 00 0 0 119896119903

]]]]]]

M1015840 = [[[[[[

119898119888119898 + 1198980119898 + 119898119888 + 1198980119898119888ℎ119888

]]]]]]

U =

1198880119891

U =

1198880119891

U =

1199061198881199060119906119891120593

F119891 =

011986511989100



Soil profiletype





Soft soil 150 1900 030 612 5

F119901 =

011986511990100

(14)


ℎ = 0811 sdot 1198972 sdot (119888 + 119892119892 ) (15)


int11990500U119879MU119889119905 + int1199050

0U119879CU119889119905 + int1199050

0UTKU119889119905

+ int11990500F119891U119889119905 + int1199050

0F119901U119889119905 = minusint1199050

0(M1015840119892)119879U119889119905

(16)


119864119868 = int11990500119898119888119888 + (119898 + 1198980) 0 + (119898 + 1198980 + 119898119888) 119891

+ 119898119888ℎ119888 119892119889119905 = int11990500119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) minus (119898 + 1198980 + 119898119888) 119892sdot 119892119889119905 = int1199050

0119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) 119892119889119905 minus int11990500(119898 + 1198980

+ 119898119888) 1198922119892119889119905

(17)



119864119863 = int11990500U119879CU119889119905

119864119865 = int11990500F119891U119889119905

119864119875 = int11990500F119901U119889119905

(18)










2 4 6 8 100Time (s)


00 02 04 06 08 10

Acce

lera

tion

(ms

2 )

(a) Chi-Chi

0 2Time (s)

4 6 8

Acce

lera

tion

(ms

2 )


00 02 04 06 08 10 12










Without SSIWith SSI

Without SSIWith SSI



00 02 04 06 08 10

Liqu

id sl

oshi

ng h

eigh

t (m

)

minus06

minus04

minus02

00

02

04

Liqu

id sl

oshi

ng h

eigh

t (m

)

2 4 6 80Time (s)

2 4 6 8 100Time (s)


Without SSIWith SSI

Without SSIWith SSI


Acce

lera

tion

(ms

2 )

Acce

lera

tion

(ms

2 )

minus600

minus400

minus200

00

200

400

600


minus50 00 50

100 150 200

2 4 6 8 100Time (s)

2 4 6 80Time (s)


Without SSIWith SSI

Without SSIWith SSI


0 2Time (s)


0 2 4 6 8

Impa

ct fo

rce (

N)


00 05 10 15 20 25

Impa

ct fo

rce (

N)

times106times106

2 4 6 8 100Time (s)

(c) Impact force

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

2 4 6 80Time (s)




0

1

2

3

4

0 2 4 6 8 10Time (s)


Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)



ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104











Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Liquid Moat wall

Structure








119897ℎ119908 lt 1333ℎ0 = 0375 119897ℎ119908 ge 13331198960 = (2120587119879119887 ) (1198980 + 119898) 1198880 = 2(2120587119879119887 ) 1205850 (1198980 + 119898)


(10)



120575int11990521199051

(119879 minus 119881) 119889119905 + int11990521199051

120575119882119899119888119889119905 = 0 (11)



119879 = 12119898119888 (119892 + 119891 + 0 + 119888 + ℎ119888)2+ 12 (1198980 + 119898) (119892 + 119891 + 0 + ℎ0)2+ 121198680 ()2


kimp kimpgp gp

uc

ℎc

ℎ0

cimp cimp

120583

c0

k0

m0 + m

mc

cc2

kc2

k0

kℎ kr

uf

cr

u0(t)

cc2

u0

ug(t)

c0

120583

cℎ

kc2

120593



minus 1198651198911205751199060 minus 1198651199011205751199060(12)



MU + CU + KU + F119891 + F119901 = minusM1015840119892 (13)

where

M

= [[[[[[

119898119888 0 119898119888 119898119888ℎ1198880 119898 + 1198980 119898 + 1198980 0119898119888 119898 + 1198980 119898119888 + 119898 + 1198980 119898119888ℎ119888119898119888ℎ119888 0 119898119888ℎ119888 119898119888ℎ2119888 + 119898ℎ20 + 1198980ℎ20 + 1198680

]]]]]]

C = [[[[[[

119888119888 minus119888119888 0 0minus119888119888 119888119888 + 1198880 0 00 0 119888ℎ 00 0 0 119888119903

]]]]]]

K = [[[[[[

119896119888 minus119896119888 0 0minus119896119888 119896119888 + 1198960 0 00 0 119896ℎ 00 0 0 119896119903

]]]]]]

M1015840 = [[[[[[

119898119888119898 + 1198980119898 + 119898119888 + 1198980119898119888ℎ119888

]]]]]]

U =

1198880119891

U =

1198880119891

U =

1199061198881199060119906119891120593

F119891 =

011986511989100



Soil profiletype





Soft soil 150 1900 030 612 5

F119901 =

011986511990100

(14)


ℎ = 0811 sdot 1198972 sdot (119888 + 119892119892 ) (15)


int11990500U119879MU119889119905 + int1199050

0U119879CU119889119905 + int1199050

0UTKU119889119905

+ int11990500F119891U119889119905 + int1199050

0F119901U119889119905 = minusint1199050

0(M1015840119892)119879U119889119905

(16)


119864119868 = int11990500119898119888119888 + (119898 + 1198980) 0 + (119898 + 1198980 + 119898119888) 119891

+ 119898119888ℎ119888 119892119889119905 = int11990500119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) minus (119898 + 1198980 + 119898119888) 119892sdot 119892119889119905 = int1199050

0119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) 119892119889119905 minus int11990500(119898 + 1198980

+ 119898119888) 1198922119892119889119905

(17)



119864119863 = int11990500U119879CU119889119905

119864119865 = int11990500F119891U119889119905

119864119875 = int11990500F119901U119889119905

(18)










2 4 6 8 100Time (s)


00 02 04 06 08 10

Acce

lera

tion

(ms

2 )

(a) Chi-Chi

0 2Time (s)

4 6 8

Acce

lera

tion

(ms

2 )


00 02 04 06 08 10 12










Without SSIWith SSI

Without SSIWith SSI



00 02 04 06 08 10

Liqu

id sl

oshi

ng h

eigh

t (m

)

minus06

minus04

minus02

00

02

04

Liqu

id sl

oshi

ng h

eigh

t (m

)

2 4 6 80Time (s)

2 4 6 8 100Time (s)


Without SSIWith SSI

Without SSIWith SSI


Acce

lera

tion

(ms

2 )

Acce

lera

tion

(ms

2 )

minus600

minus400

minus200

00

200

400

600


minus50 00 50

100 150 200

2 4 6 8 100Time (s)

2 4 6 80Time (s)


Without SSIWith SSI

Without SSIWith SSI


0 2Time (s)


0 2 4 6 8

Impa

ct fo

rce (

N)


00 05 10 15 20 25

Impa

ct fo

rce (

N)

times106times106

2 4 6 8 100Time (s)

(c) Impact force

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

2 4 6 80Time (s)




0

1

2

3

4

0 2 4 6 8 10Time (s)


Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)



ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104











Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










kimp kimpgp gp

uc

ℎc

ℎ0

cimp cimp

120583

c0

k0

m0 + m

mc

cc2

kc2

k0

kℎ kr

uf

cr

u0(t)

cc2

u0

ug(t)

c0

120583

cℎ

kc2

120593



minus 1198651198911205751199060 minus 1198651199011205751199060(12)



MU + CU + KU + F119891 + F119901 = minusM1015840119892 (13)

where

M

= [[[[[[

119898119888 0 119898119888 119898119888ℎ1198880 119898 + 1198980 119898 + 1198980 0119898119888 119898 + 1198980 119898119888 + 119898 + 1198980 119898119888ℎ119888119898119888ℎ119888 0 119898119888ℎ119888 119898119888ℎ2119888 + 119898ℎ20 + 1198980ℎ20 + 1198680

]]]]]]

C = [[[[[[

119888119888 minus119888119888 0 0minus119888119888 119888119888 + 1198880 0 00 0 119888ℎ 00 0 0 119888119903

]]]]]]

K = [[[[[[

119896119888 minus119896119888 0 0minus119896119888 119896119888 + 1198960 0 00 0 119896ℎ 00 0 0 119896119903

]]]]]]

M1015840 = [[[[[[

119898119888119898 + 1198980119898 + 119898119888 + 1198980119898119888ℎ119888

]]]]]]

U =

1198880119891

U =

1198880119891

U =

1199061198881199060119906119891120593

F119891 =

011986511989100



Soil profiletype





Soft soil 150 1900 030 612 5

F119901 =

011986511990100

(14)


ℎ = 0811 sdot 1198972 sdot (119888 + 119892119892 ) (15)


int11990500U119879MU119889119905 + int1199050

0U119879CU119889119905 + int1199050

0UTKU119889119905

+ int11990500F119891U119889119905 + int1199050

0F119901U119889119905 = minusint1199050

0(M1015840119892)119879U119889119905

(16)


119864119868 = int11990500119898119888119888 + (119898 + 1198980) 0 + (119898 + 1198980 + 119898119888) 119891

+ 119898119888ℎ119888 119892119889119905 = int11990500119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) minus (119898 + 1198980 + 119898119888) 119892sdot 119892119889119905 = int1199050

0119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) 119892119889119905 minus int11990500(119898 + 1198980

+ 119898119888) 1198922119892119889119905

(17)



119864119863 = int11990500U119879CU119889119905

119864119865 = int11990500F119891U119889119905

119864119875 = int11990500F119901U119889119905

(18)










2 4 6 8 100Time (s)


00 02 04 06 08 10

Acce

lera

tion

(ms

2 )

(a) Chi-Chi

0 2Time (s)

4 6 8

Acce

lera

tion

(ms

2 )


00 02 04 06 08 10 12










Without SSIWith SSI

Without SSIWith SSI



00 02 04 06 08 10

Liqu

id sl

oshi

ng h

eigh

t (m

)

minus06

minus04

minus02

00

02

04

Liqu

id sl

oshi

ng h

eigh

t (m

)

2 4 6 80Time (s)

2 4 6 8 100Time (s)


Without SSIWith SSI

Without SSIWith SSI


Acce

lera

tion

(ms

2 )

Acce

lera

tion

(ms

2 )

minus600

minus400

minus200

00

200

400

600


minus50 00 50

100 150 200

2 4 6 8 100Time (s)

2 4 6 80Time (s)


Without SSIWith SSI

Without SSIWith SSI


0 2Time (s)


0 2 4 6 8

Impa

ct fo

rce (

N)


00 05 10 15 20 25

Impa

ct fo

rce (

N)

times106times106

2 4 6 8 100Time (s)

(c) Impact force

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

2 4 6 80Time (s)




0

1

2

3

4

0 2 4 6 8 10Time (s)


Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)



ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104











Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Soil profiletype





Soft soil 150 1900 030 612 5

F119901 =

011986511990100

(14)


ℎ = 0811 sdot 1198972 sdot (119888 + 119892119892 ) (15)


int11990500U119879MU119889119905 + int1199050

0U119879CU119889119905 + int1199050

0UTKU119889119905

+ int11990500F119891U119889119905 + int1199050

0F119901U119889119905 = minusint1199050

0(M1015840119892)119879U119889119905

(16)


119864119868 = int11990500119898119888119888 + (119898 + 1198980) 0 + (119898 + 1198980 + 119898119888) 119891

+ 119898119888ℎ119888 119892119889119905 = int11990500119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) minus (119898 + 1198980 + 119898119888) 119892sdot 119892119889119905 = int1199050

0119898119888 (119892 + 119891 + ℎ119888 + 119888)

+ (119898 + 1198980) (0 + 119891 + 119892) 119892119889119905 minus int11990500(119898 + 1198980

+ 119898119888) 1198922119892119889119905

(17)



119864119863 = int11990500U119879CU119889119905

119864119865 = int11990500F119891U119889119905

119864119875 = int11990500F119901U119889119905

(18)










2 4 6 8 100Time (s)


00 02 04 06 08 10

Acce

lera

tion

(ms

2 )

(a) Chi-Chi

0 2Time (s)

4 6 8

Acce

lera

tion

(ms

2 )


00 02 04 06 08 10 12










Without SSIWith SSI

Without SSIWith SSI



00 02 04 06 08 10

Liqu

id sl

oshi

ng h

eigh

t (m

)

minus06

minus04

minus02

00

02

04

Liqu

id sl

oshi

ng h

eigh

t (m

)

2 4 6 80Time (s)

2 4 6 8 100Time (s)


Without SSIWith SSI

Without SSIWith SSI


Acce

lera

tion

(ms

2 )

Acce

lera

tion

(ms

2 )

minus600

minus400

minus200

00

200

400

600


minus50 00 50

100 150 200

2 4 6 8 100Time (s)

2 4 6 80Time (s)


Without SSIWith SSI

Without SSIWith SSI


0 2Time (s)


0 2 4 6 8

Impa

ct fo

rce (

N)


00 05 10 15 20 25

Impa

ct fo

rce (

N)

times106times106

2 4 6 8 100Time (s)

(c) Impact force

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

2 4 6 80Time (s)




0

1

2

3

4

0 2 4 6 8 10Time (s)


Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)



ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104











Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













2 4 6 8 100Time (s)


00 02 04 06 08 10

Acce

lera

tion

(ms

2 )

(a) Chi-Chi

0 2Time (s)

4 6 8

Acce

lera

tion

(ms

2 )


00 02 04 06 08 10 12










Without SSIWith SSI

Without SSIWith SSI



00 02 04 06 08 10

Liqu

id sl

oshi

ng h

eigh

t (m

)

minus06

minus04

minus02

00

02

04

Liqu

id sl

oshi

ng h

eigh

t (m

)

2 4 6 80Time (s)

2 4 6 8 100Time (s)


Without SSIWith SSI

Without SSIWith SSI


Acce

lera

tion

(ms

2 )

Acce

lera

tion

(ms

2 )

minus600

minus400

minus200

00

200

400

600


minus50 00 50

100 150 200

2 4 6 8 100Time (s)

2 4 6 80Time (s)


Without SSIWith SSI

Without SSIWith SSI


0 2Time (s)


0 2 4 6 8

Impa

ct fo

rce (

N)


00 05 10 15 20 25

Impa

ct fo

rce (

N)

times106times106

2 4 6 8 100Time (s)

(c) Impact force

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

2 4 6 80Time (s)




0

1

2

3

4

0 2 4 6 8 10Time (s)


Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)



ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104











Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Without SSIWith SSI

Without SSIWith SSI



00 02 04 06 08 10

Liqu

id sl

oshi

ng h

eigh

t (m

)

minus06

minus04

minus02

00

02

04

Liqu

id sl

oshi

ng h

eigh

t (m

)

2 4 6 80Time (s)

2 4 6 8 100Time (s)


Without SSIWith SSI

Without SSIWith SSI


Acce

lera

tion

(ms

2 )

Acce

lera

tion

(ms

2 )

minus600

minus400

minus200

00

200

400

600


minus50 00 50

100 150 200

2 4 6 8 100Time (s)

2 4 6 80Time (s)


Without SSIWith SSI

Without SSIWith SSI


0 2Time (s)


0 2 4 6 8

Impa

ct fo

rce (

N)


00 05 10 15 20 25

Impa

ct fo

rce (

N)

times106times106

2 4 6 8 100Time (s)

(c) Impact force

Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

minus015

minus010

minus005

000

005

010

015

Disp

lace

men

t (m

)

2 4 6 80Time (s)




0

1

2

3

4

0 2 4 6 8 10Time (s)


Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)



ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104











Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

1

2

3

4

0 2 4 6 8 10Time (s)


Chi-Chi

0 2 4 6 8

10 12 14 16 18

0 2 4 6 8Time (s)



ergy

(Nmiddotm

)

Ener

gy (N

middotm)

times105 times104











Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Without SSIWith SSI

Without SSIWith SSI


EF

(Nmiddotm

)

EF

(Nmiddotm

)

0 2 4 6 8

10 12 14 16 18

0

2

4

6

8

10

12

14

2 4 6 8 100Time (s)

2 4 6 80Time (s)

times104 times104


Without SSIWith SSI

Without SSIWith SSI


(Nmiddotm

)

EP

(Nmiddotm

)

0 4 8

12 16 20 24 28 32 36

0

1

2

3

4

2 4 6 80Time (s)

0 2 4Time (s)

6 8 10

times104 times104


Without SSIWith SSI

Without SSIWith SSI


0 2 4 6 8 10Time (s)

0 2 4 6 8Time (s)

ED

(Nmiddotm

)

EP

(Nmiddotm

)

00 05 10 15 20 25 30 35 40

00

05

10

15

20

25 times104times104








00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











00 02 04 06 08 10 12

Liqu

id sl

oshi

ng h

eigh

t (m

)

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60 70 80 90

000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

gp (m)



000

002

004

006

008

010

012

014

016

018

020

022

024

026

028

minus2 0 2 4 6 8

10 12

Impa

ct fo

rce (

N)

gp (m)

(c) Impact force


00

02

04

06

08

10

Liqu

id sl

oshi

ng h

eigh

t (m

)

002 004 006 008 010 012 014 016


120583


Acce

lera

tion

(ms

2 )

0 10 20 30 40 50 60

002 004 006 008 010 012 014 016


120583


0 1 2 3 4 5 6 7 8 9

Impa

ct fo

rce (

N)

002 004 006 008 010 012 014 016


120583

(c) Impact force



008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










008 010 012 014016

018

010

012

014

016

018

020

022

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


01000

01150

01300

01450

01600

01750

01900

02050

02200


008 010 012 014016 018

006

008

010

012

010012

014016

018020

Max

imum

hor

izon

tal d

ispla

cem

ent (

m)

Gap siz

e (m)


006000

006750

007500

008250

009000

009750

01050

01125

01200






5 Conclusions










Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Competing Interests


Acknowledgments


References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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