Research Article Vibration Control of Nuclear Power Plant ...downloads.hindawi.com/journals/stni/2016/5014093.pdf · Research Article Vibration Control of Nuclear Power Plant Piping

Research ArticleVibration Control of Nuclear Power Plant Piping System UsingStockbridge Damper under Earthquakes

Seongkyu Chang1 Weipeng Sun2 Sung Gook Cho3 and Dookie Kim4

1Academic-Industry Cooperation Foundation Kunsan National University Jeonbuk Republic of Korea2Department of Mechanics and Engineering Science School of Mathematics Jilin University Changchun 130012 China3RampD Center Innose Tech Co Ltd Incheon 406-840 Republic of Korea4Department of Civil Engineering Kunsan National University Jeonbuk Republic of Korea

Correspondence should be addressed to Seongkyu Chang s9752033gmailcom

Received 6 September 2016 Accepted 3 November 2016

Academic Editor Eugenijus Uspuras

Copyright copy 2016 Seongkyu Chang 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

Generally the piping system of a nuclear power plant (NPP) has to be designed for normal loads such as dead weight internalpressure temperature and accidental loads such as earthquake In the proposed paper effect of Stockbridge damper to mitigatethe response of piping system of NPP subjected to earthquake is studied Finite element analysis of piping system with and withoutStockbridge damper using commercial software SAP2000 is performed Vertical and horizontal components of earthquakes suchas El Centro California and Northridge are used in the piping analysis A sine sweep wave is also used to investigate the controleffects on the piping system under wide frequency range It is found that the proposed Stockbridge damper can reduce the seismicresponse of piping system subjected to earthquake loading

1 Introduction

Usually nuclear power plant (NPP) piping system needs tobe designed for various loads such as dead weight internalpressure temperature and accidental loads as well as forseismic loads These loads can occur inside the nuclearpower plant piping system and affect the operation of theplant Researchers have investigated ways to reduce pipevibration using various devices including snubbers pipehangers support systems and isolators Kunieda et al [1]proposed three control devices for piping systems to increasethe damping ratio a direct damper vibration absorber andconnecting damper Olson and Tang [2] proposed snubberand seismic stops to suppress the vibration of a nuclear powerplant piping system however it is very difficult to frequentlyinspect snubbers in the high-radiation conditions in a nuclearpower plant and the cost for installation was prohibitivelyexpensive Shimuzu et al [3] developed a seismic responseanalysis procedure of the piping system and performed anevaluation of the piping response by comparing simulatedresults and tested results Park et al [4] performed the shaking

table test and simulation for the main steam and feedwa-ter lines with conventional snubbers and energy absorb-ing supports Parulekar et al [5] performed analytical andexperimental research to reduce the vibration of the pipingand equipment of a nuclear power plant using elastoplasticdampers (EPD) Abe et al [6] conducted the seismic provingtest of Lead Extrusion Damper (LED) and developed thecharacteristic evaluation formula for LED Moreover Fujitaet al [7] proposed a method of nonlinear seismic responseanalysis for a piping system using a combination of theFinite Element Method (FEM) and the Differential AlgebraicEquations (DAE) Bakre et al [8] inspected the effectivenessof sliding friction dampers for piping systems using analyticaland experimental methods Bakre et al [9] attempted tooptimize x-plate dampers and the seismic effectiveness ofthese dampers for a piping system in industrial installations

In this study a Stockbridge damper (SBD) originallydeveloped by Stockbridge in 1925 [10] is suggested to sup-press the vibration of a nuclear power plant piping systemunder earthquakesWagner et al [11] established a theoreticalanalysis of the response characteristics of SBD to verify

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2016 Article ID 5014093 12 pageshttpdxdoiorg10115520165014093

2 Science and Technology of Nuclear Installations

X

Y

Z

(a) 3D view

X

Y

Z

(b) Plane view

XY

Z

(c) Elevation view

Figure 1 Nuclear power plant piping system for earthquake analysis

a theoretical predictions experimental testThe SBDwas usedto reduce the vibration of slender structures in wind such asoverhead transmission lines and stayed cables [12ndash15] Vec-chiarelli et al [12] performednumerical analysis to predict thevertical steady-state aeolian vibration of a single conductorspan attached with a Stockbridge-type damper ThereafterBarry [13] developed a finite element model to evaluate thevibrational response of a single conductor with a Stockbridgedamper and investigate the effects of the Stockbridge damperUrushadze et al [14] conducted experimental and numericalverification of wind-induced vibration of hangers on thepedestrian bridge and suggested to equip the hangers withStockbridge dampers To investigate the linear and nonlineardynamic behavior of asymmetric Stockbridge damper anexperimental test and a numerical analysis were performedby N Barbieri and R Barbieri [15]

In this study a piping system (ASCE CLASS1 SA312GRADE TP316 SCH) was installed in identical conditions tothose in a real nuclear power plant andwas used to investigatethe control performance of the SBD Finite element analysisof piping system with and without Stockbridge damperwas performed using commercial software SAP2000 A sinesweep wave was used to investigate the control effects onthe piping system under wide frequency range In order toconfirm the control effects of the Stockbridge damper underrandom earthquake vibration the three selective (El CentroCalifornia and Northridge) earthquakes were used in thisinvestigation

2 Piping System

21 Outline of Piping System The nuclear power plant pipingsystem was composed of 2- and 3-inch sized pipes the lengthof the axis of ordinates is 178m the end of the pipe tip wasfixed and 2 reducers were modeled as hinge conditions It isassumed that the inner space of the pipe was filled with waterThe water was modeled as an additional mass

Table 1 Material properties

Item Value UnitYoungrsquos modulus 199000 MPaPoissonrsquos ratio 031 mdashSteel density 7850 kgm3

Water density 1000 kgm3

Table 2 Section properties

Pipe size(in)

External diameter(mm)

Internal diameter(mm)

Thickness(mm)

2 603 428 8743 889 666 1113

Figure 1 shows the piping system modeled by SAP2000The material properties and cross-sectional properties of thepipe are shown in Tables 1 and 2 All properties were appliedas the values suggested by the design criteria

22 Free Vibration Analysis A free vibration analysis wasperformed with respect to the piping system in order tocalculate the parameters of the damper such as mass fre-quency ratio and damping ratio From the free vibrationanalysis the first to third modes show very complex modalshapes which are a combination of horizontal and verticalshapes as shown in Figures 2ndash4 The first and third modeshapes are predominantly horizontal mode shaped and thesecond mode shape is predominantly vertical mode shapedThe maximum amplitudes of where the damping device willbe installed were marked using a red color dot The dynamicproperties of the piping system calculated from free vibrationanalysis results are shown in Table 3

Since the main control target modes are the first to thirdmodes each generalized mass was calculated up to the thirdmode

Science and Technology of Nuclear Installations 3

Table 3 Dynamic properties of the piping system

Mode Period (sec) Frequency (Hz) Modal participating mass ratio Generalized mass (kg)119909 119910 1199111st 0575 1741 00003 03800 00642 1822nd 0471 2125 00000 00641 04100 1703rd 0190 5254 00020 00185 00002 1664th 0173 5779 00007 00001 00005 mdash5th 0102 9806 00280 00091 00000 mdash6th 0086 11563 00000 00003 00183 mdash7th 0074 13426 00128 01200 00004 mdash8th 0059 16869 03000 00096 00211 mdash

X

Y

Z

(a) Plane view

XY

Z

(b) Elevation view

Figure 2 First mode shape

X

Y

Z

(a) Plane view

XY

Z

(b) Elevation view

Figure 3 Second mode shape

X

Y

Z

(a) Plane view

XY

Z

(b) Elevation view

Figure 4 Third mode shape

3 Design of Dampers

We utilized a two-step process to design a damper to reducethe vibration of the piping system The first step is thecalculation of the mass ratio frequency ratio and dampingratio of the damper Then in the second step the specificdesign of the SBD is done The design parameters of thedamper are determined from the eigenvalue analysis resultsAccording to Den Hartogrsquos formula the mass ratio optimum

frequency ratio and optimum damping ratio are calculatedas follows [16]

120583 = 81205852eff1 minus 41205852eff 120574opt = 11 + 120583 120585opt = 12radic 312058321 + 3120583

(1)


Mass

Messenger cable

For y-direction control For z-direction control

Connection part

Piping system

Z

X

Figure 5 Components of a Stockbridge damper

where 120585eff is the effective damping ratio of the piping system120583 is the mass ratio 120574opt is the optimum frequency ratio and120585opt is the optimum damping ratio of the damper

31 Stockbridge Damper TheSBD is composed of amass partandmessenger cable parts as shown in the SBD cross sectionin Figure 5 The messenger cable is comprised of several steelwire strands and can dissipate the energy of the vibrationthrough strand friction In this paper both sides of the SBDplay a different role The left part of the SBD reduces the 119910-direction vibration of the piping system while the right partof the SBD suppresses the 119911-direction vibration of the pipingsystem

The equation of motion for SBD is given as

119872 + 119862 + 119870119909 = 0 (2)

where 119872 is the mass matrix 119862 is the damping matrix and119870 is the stiffness matrix and and 119909 are the accelerationvelocity and displacement of the SBD respectively

Undamped natural frequencies of the SBD system areobtained by [11]

1205961 = (ℎ minus 1198862119898120588 )12

1205962 = (ℎ + 1198862119898120588 )12

120588 = (119903119897 )2 ℎ = (1 + 120588) 11989611 + 119896221198972 minus 211989612119897 119886 = radicℎ2 minus 41205881198972 (1198961111989622 minus 119896212)

(3)

where 120596119894 is the frequency of the SBD 119898 is the mass 119903 isthe radius of gyration of mass 119897 is the distance betweenthe attachment point and the center of gravity of the massand 119896119894119895 is the bending stiffness of messenger cable (where119894 119895 = 1 2 3 ) The basic design for the SBD was calculatedusing the above equations and the target frequency was then

Table 4 Properties of SBD

Parameters SBD (119910-direction) SBD (119911-direction)Mass ratio 0022 0024Mass (kg) 40 40Frequency ratio 0978 0977Damping ratio 015 015Messenger cable length (m) 024 021

adjusted by fine tuning The properties of the SBD are shownin Table 4

4 Base Excitation

41 Sine Sweep Wave In order to investigate the frequencyranges of the piping system a sine sweeping wave with peakacceleration of 10msec2 varying from 01Hz to 20Hz wasapplied to the nuclear power plant piping system with andwithout the SBD for 119910- and 119911-directions (Figure 6)42 Earthquake Ground Motion In this study recordedearthquakes were used to verify that the proposed SBDcan reduce the vibration response of the nuclear powerplant piping system El Centro California and Northridgeearthquakes were selected for dynamic analysis El Centroearthquakes of the 119909- 119910- and 119911-axis direction were usedto check the horizontal and vertical behavior of the pipingsystem The earthquake time history has a 50-second dura-tion and 002-second time steps Peak ground accelerationswere scaled to 034 g 021 g and 021 g for the 119909- 119910- and 119911-axis directions respectivelyThe timehistory acceleration andresponse spectrum of the ground motion in each directionwere shown in Figure 7 While the horizontal earthquakeshave an energy distribution between 1Hz and 5Hz verticalearthquakes have more vibration energy in 10Hz

Vertical earthquakes were scaled to fit 12 of PGA of thehorizontal ground motion for California and Northridgeearthquakes Therefore the PGAs of California andNorthridge earthquakes were scaled from 015 g to 0075 gand from 034 g to 017 g in the vertical direction respectivelyThe ground motion of each direction and response spectrumare shown in Figures 8 and 9


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

05

1

Sweep

minus05

minus1

Acc

(ms

ec2)

(a) Sweep wave

Sweep

0 2 4 6 8 10 12 14 16 18 20Frequency (Hz)

0

05

1

15

FFT

(ms

)

(b) FFT

Figure 6 Sine sweep wave and its FFT

0 5 10 15 20 25 30 35 40 45 50

024

El Centro x-dir

0 5 10 15 20 25 30 35 40 45 50

024

El Centro y-dir

0 5 10 15 20 25 30 35 40 45 50Time (sec)

Time (sec)

Time (sec)

02

El Centro z-dir

Acc

(ms

ec2)

Acc

(ms

ec2)

Acc

(ms

ec2)

minus2

minus2

minus4

minus2

minus4

(a) El Centro earthquake

Frequency (Hz)

x-diry-dirz-dir

100

101

10minus1

0

1

2

3

4

5

6

7

8

9

Acc

(ms2)

(b) Response spectrum

Figure 7 El Centro earthquake and its FFT

5 Results and Discussion

51 Response of Piping System Subjected to Sine Sweep Excita-tion The accelerations of the piping system were measuredin the maximum amplitude when the SBD was not installedon the piping system (red spot in Figures 2ndash4) Figure 10shows the time history response and response spectrum ofthe 119910-directional response after inputting the signal in the 119910-directionThis shows that the firstmode (19Hz) is dominantHowever in the case of Figure 11 the 119911-direction responseof the piping system after applying the 119910-directional wave isshownThis simultaneously shows the peak in the first modeshape at 19Hz (119910-directional mode) and the second modeshape at 23Hz (119911-directional mode) of the piping systemunder the sine sweep wave because the modal shape of thepiping systemwasmixed Figure 13 also shows the same trendwith inverse load conditions from those in Figure 11 Figure 12

shows the same trend with Figure 10 From the results ofthe sine sweep wave it is confirmed that the proposed SBDcan reduce the vibration in all frequency domains (01 Hz to20Hz) Based on the given results it is evident that having awide frequency range is one advantage of the SBD

52 Response of Piping System Subjected to EarthquakesAn earthquake analysis was performed to investigate theapplicability with respect to the piping system and to con-firm the vibration mitigation of the piping system withand without the SBD under the recorded earthquakes Theaccelerations of the piping system were measured for themaximum amplitude when the SBD was not installed on thepiping system (red spot in Figures 2ndash4) Figure 14 shows thetime history response and frequency domain response of thepiping system with and without the SBD in the 119909- 119910- and


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

1

2

California y-dir

0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

1

2

California z-dir

Acc

(ms

ec2)

Acc

(ms

ec2)

minus2

minus1

minus2

minus1

(a) California earthquake

Frequency (Hz)

y-dirz-dir

100

101

10minus1

0

1

2

3

4

5

6

Acc

(ms2)


Figure 8 California earthquake and its response spectrum

0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Northridge y-dir

0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Northridge z-dir

Acc

(ms

ec2)

Acc

(ms

ec2)

minus4

minus2

minus4

minus2

(a) Northridge earthquake

Frequency (Hz)

y-dirz-dir

100

101

10minus1

0

1

2

3

4

5

6

7

8

9

10

Acc

(ms2)


Figure 9 Northridge earthquake and its response spectrum

119911-axis directions when El Centro earthquake was applied tothe system

The 119909-directional vibration of the piping system appearedto be almost invisible when the SBD was installed (Fig-ure 14(a)) The maximum acceleration decreased from158ms2 to 002ms2 and the root mean square (RMS) wasreduced from 013ms2 to 0002ms2 in the 119909-direction Eachdecreasing ratio was 990 and 985 respectively In thecase of the 119910-direction response the maximum accelerationdecreased from 652ms2 to 197ms2 and RMS was reduced

from 124ms2 to 029ms2 when the SBD was appliedTable 5 shows themaximum acceleration RMS response andits decreasing ratio where the SBDwas installed In this paperthe maximum acceleration and RMS were used to evaluatethe vibration of the piping systemThe RMS are calculated asfollows

RMS = radic 1119873119873sum119899=1

1003816100381610038161003816acc11989910038161003816100381610038162 (4)


Table 5 Results for El Centro earthquake

Direction Maximum acceleration (ms2) RMS acceleration (ms2)Uncontrolled Controlled Decreasing ratio () Uncontrolled Controlled Decreasing ratio ()119909 1577 0016 990 0126 0002 985119910 6523 1973 698 1237 0285 769119911 3538 3145 111 0460 0260 435

Time (sec)

UncontrolledControlled

10

5

0

minus5

minus10

1009080706050403020100

Acc

(ms

ec2)

(a) Acceleration response

Frequency (Hz)


100

101

10minus1

0

10

20

30

40

Acc

(ms2)


Figure 10 Response of piping system subjected to sine sweep wave (119910-direction load and response)

Time (sec)


1009080706050403020100

0

2

4

Acc

(ms

ec2)

minus4

minus2


Frequency (Hz)


100

101

10minus1

0

5

10

15

20

Acc

(ms2)


Figure 11 Response of piping system subjected to sine sweep wave (119910-direction load versus 119911-direction response)

Time (sec)


1009080706050403020100

Acc

(ms

ec2)

10

5

0

minus5

minus10


Frequency (Hz)


100

101

10minus1

0

10

20

30

40

50

Acc

(ms2)




Time (sec)


1009080706050403020100

Acc

(ms

ec2)

0

2

4

minus4

minus2


Frequency (Hz)UncontrolledControlled

10

15

20

5

0

100

101

10minus1

Acc

(ms2)



Frequency (Hz)



100

101

10minus10 5 10 15 20 25 30 35 40 45 50

Time (sec)

0

1

2

minus1

minus2

Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)

(a) 119909-direction

0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10

Acc

(ms

ec2)



0

10

20

30

40

Acc

(ms2)

(b) 119910-direction

0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4

Acc

(ms

ec2)



0

5

10

15

Acc

(ms2)

(c) 119911-direction

Figure 14 Response of piping system subjected to El Centro earthquake


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

1

2

3

Frequency (Hz)

0

2

4

6

8

10

100

101

10minus1

minus1

minus2

minus3



Acc

(ms

ec2)

Acc

(ms2)


Figure 15 Response of piping system subjected to California earthquake

where 119873 is the length of data and acc119899 is the acceleration of119899th time stepThe RMS represents the amplitude related withan energy amount which indicates the destructive ability ofthe vibration

The 119911-directional El Centro earthquake shows a largeamount of energy on the adjacent 10Hz unlike earth-quakes of the other directions (Figure 7(a)) Although theproposed SBD was not designed with respect to that fre-quency area nevertheless the control effects of the dampercan be confirmed based on the peak acceleration andresponse spectrum Since the SBD was not designed for 119909-directional response the control system has some effectson the responses of 119909-directions This phenomenon can beexplained by the reason of the piping system having complexmodal shapes and coupled responses In other words if 119910-direction and 119911-direction responses of the piping system canoccur by earthquake in 119909-direction then it is obvious thatthe SBD can be capable of suppressing the vibration in 119909-direction with the other both directions instead of not beingdesigned for 119909-direction

Figures 15 and 16 show the time history response andfrequency domain response of the nuclear power plant pipingsystem with and without the SBD in the 119910- and 119911-axisdirections under California andNorthridge earthquakesTheacceleration response of both earthquakes was considerablysuppressed by the proposed SBD With respect to Californiaearthquake the maximum acceleration of the piping system

decreased from 322ms2 to 117ms2 and RMS response wasreduced from 067ms2 to 019ms2 in the 119910-direction Eachdecreasing ratio was 638 and 716 respectively In thecase of the 119911-direction the decreasing ratio of the maximumacceleration and RMS response decreased by 743 and734 respectively

This demonstrates the good control performance of theSBD for Northridge earthquake as shown in Figure 16The maximum acceleration and RMS response decreased by602 and 740 in the 119910-direction respectively and 585and 719 in the 119911-direction respectively The maximumacceleration and RMS response for each earthquake areshown in Tables 6 and 7

Figure 17 shows the response of the piping system in the 119911-direction under the 119910-directional El Centro earthquake andthe response of the piping system in the 119910-direction underthe 119911-directional El Centro earthquake It can be seen thatthe response reduction of the piping system in Figure 17is more noticeable than the trend shown in Figures 14ndash16 While the control effects of the SBD in Figures 14ndash16show extremely effective behavior at tuned frequencies (firstand second mode) the frequency response of Figure 17 is2Hz which shows a wide range of frequency response Theresponse decreasing ratio of the piping systemwas largewhenthe load direction and response direction were differentThis is because the SBD in this paper was actually designedfor first and second frequency modes therefore the SBD


Table 6 Results for California earthquake

Direction Maximum acceleration (ms2) RMS acceleration (ms2)Uncontrolled Controlled Decreasing ratio () Uncontrolled Controlled Decreasing ratio ()119910 3217 1165 638 0667 0190 716119911 2256 0580 743 0350 0093 734

Table 7 Results for Northridge earthquake


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10



Acc

(ms

ec2)

0

10

20

30

40

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)


Figure 16 Response of piping system subjected to Northridge earthquake

extremely suppressed the vibration of the piping systemHowever that the SBD can also reduce vibrations beyondthe design frequency range was already confirmed in ourprevious results The results of California earthquake alsoshow a similar trend with those of El Centro earthquake(Figure 18) The directional results for both earthquakes aresummarized in Tables 8 and 9 The reduction ratio of allresponses is more than 90

6 ConclusionFrom the study performed SBD is recommended to controlthe seismic response of NPP piping system Effect of SBD

to control the seismic response of piping system is demon-strated considering El Centro California and Northridgeearthquake excitations The piping system (ASCE CLASS1SA312 GRADE TP316 SCH) was modeled under the sameconditions as in an actual nuclear power plant The SBD wasdesigned for low order frequency modes using free vibra-tion analysis results The controlled responses of the timeand frequency domain were compared with uncontrolledresponses of the piping system under horizontal and verticalearthquakes It was confirmed through sine sweep waveanalysis that the proposed damper can reducewide frequencyvibration responses


0 5 10 15 20 25 30 35 40 45 50

0

05

1

Frequency (Hz)Time (sec)10

010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)

(a) 119910-direction response under 119911-direction load

0 5 10 15 20 25 30 35 40 45 50

0

2

4


010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)

(b) 119911-direction response under 119910-direction load


0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

1

2


010

110

minus1

minus1

minus2



Acc

(ms

ec2)

0

2

4

6

8

10

Acc

(ms2)




Table 8 Directional results for El Centro earthquake

Direction Maximum acceleration (ms2) RMS acceleration (ms2)Load Resp Uncontrolled Controlled Decreasing ratio () Uncontrolled Controlled Decreasing ratio ()119911 119910 0838 0082 903 0169 0008 952119910 119911 3132 0114 963 0618 0018 971

Table 9 Directional results for California earthquake


In the earthquake results the maximum accelerationdeclined by about 99 69 and 11 in each directionunder El Centro earthquake respectively The maximumaccelerations decreased by 63 in 119910-direction and 74 in119911-direction under California earthquake In the case of theNorthridge earthquake reductions of each acceleration werefound to be 60 and 58 in 119910-direction and 119911-directionsuccessively

From the earthquake response analysis results it wasfound that the proposed SBD can reduce not only the targetedvibration modes of the piping system but also other modesunder earthquakes Most importantly it was also confirmedthat the proposed SBD can effectively reduce the vibration ofa nuclear power plant piping system under earthquakes

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by the National Research Foun-dation of Korea Grant funded by the Korean Government(NRF-2014R1A2A1A10049538) and the Nuclear Power CoreTechnology Development Program of the Korea Institute ofEnergy Technology Evaluation and Planning (KETEP) grantfinancial resource from the Ministry of Trade Industry ampEnergy Republic of Korea (no 20131520400080)

References

[1] M Kunieda T Chiba and H Kobayashi ldquoPositive use ofdamping devices for piping systemsmdashsome experiences andnew proposalsrdquo Nuclear Engineering and Design vol 104 no2 pp 107ndash120 1987

[2] D E Olson and Y K Tang ldquoDecreasing snubber inserviceinspection costs through snubber reduction and improved testlimitsrdquoNuclear Engineering andDesign vol 107 no 1-2 pp 183ndash199 1988

[3] N Shimuzu K Suzuki T Watanabe N Ogawa and HKobayashi ldquoLarge scale shaking table test on modal responsesof 3D piping system with friction supportrdquo Seismic EngineeringASME PVP vol 340 pp 269ndash275 1996

[4] N Park G DeGrassi C Hofmayer and P Bezler ldquoAnalysisof nuclear piping system seismic tests with conventional and

energy absorbing supportsrdquo in Proceedings of the InternationalConference on Structural Mechanics in Reactor Technology pp269ndash275 Lyon France 1997

[5] Y M Parulekar G R Reddy K K Vaze and H S KushwahaldquoElasto-plastic damper for passive control of seismic responseof piping systemsrdquo BARC Internal Report Reactor SafetyDivision 2002

[6] HAbe I Ichihashi K Kuroda T Iwatsubo andK Tai ldquoSeismicproving test of heavy component with energy absorbing sup-portrdquo in Proceedings of the International Conference on GlobalEnvironment and Advanced Nuclear Power Plants Kyoto JapanSeptember 2003

[7] K Fujita T Kimura and Y Ohe ldquoSeismic response analysisof piping systems with nonlinear supports using differentialalgebraic equationsrdquo Journal of Pressure Vessel TechnologyTransactions of the ASME vol 126 no 1 pp 91ndash97 2004

[8] S V Bakre R S Jangid and G R Reddy ldquoSeismic response ofpiping system with isolation devicesrdquo in Proceedings of the 13thWorld Conference on Earthquake Engineering Paper no 2676Vancouver Canada August 2004

[9] S V Bakre R S Jangid and G R Reddy ldquoOptimum X-platedampers for seismic response control of piping systemsrdquo inProceedings of the 4th International Conference on StructuralStability and Dynamics 2012

[10] G Stockbridge ldquoVibration Damperrdquo Patent No 1675391 USAPatent Office 1925

[11] H Wagner V Ramamurti R V R Sastry and K HartmannldquoDynamics of stockbridge dampersrdquo Journal of Sound andVibration vol 30 no 2 pp 207ndash220 1973

[12] J Vecchiarelli I G Currie and D G Havard ldquoComputationalanalysis of aeolian conductor vibration with a stockbridge-typedamperrdquo Journal of Fluids and Structures vol 14 no 4 pp 489ndash509 2000

[13] O Barry Finite element analysis of a single conductor with a stockbridge damper under aeolian vibration [MS thesis] RyersonUniversity 2010

[14] S Urushadze M Pirner S Pospisil and R Kral ldquoExperimentaland numerical verification of vortex-induced vibration of hang-ers on the footbridgerdquo in Proceedings of the 18th InternationalConference Engineering Mechanics Svratka Czech Republic2012

[15] N Barbieri and R Barbieri ldquoDynamic analysis of stockbridgedamperrdquo Advances in Acoustics and Vibration vol 2012 ArticleID 659398 8 pages 2012

[16] J P Den Hartog Mechanical Vibrations McGraw-Hill BookCompany New York NY USA 3rd edition 1947

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International Journal of

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Journal ofEngineeringVolume 2014

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International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


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Figure 1 Nuclear power plant piping system for earthquake analysis

a theoretical predictions experimental testThe SBDwas usedto reduce the vibration of slender structures in wind such asoverhead transmission lines and stayed cables [12ndash15] Vec-chiarelli et al [12] performednumerical analysis to predict thevertical steady-state aeolian vibration of a single conductorspan attached with a Stockbridge-type damper ThereafterBarry [13] developed a finite element model to evaluate thevibrational response of a single conductor with a Stockbridgedamper and investigate the effects of the Stockbridge damperUrushadze et al [14] conducted experimental and numericalverification of wind-induced vibration of hangers on thepedestrian bridge and suggested to equip the hangers withStockbridge dampers To investigate the linear and nonlineardynamic behavior of asymmetric Stockbridge damper anexperimental test and a numerical analysis were performedby N Barbieri and R Barbieri [15]

In this study a piping system (ASCE CLASS1 SA312GRADE TP316 SCH) was installed in identical conditions tothose in a real nuclear power plant andwas used to investigatethe control performance of the SBD Finite element analysisof piping system with and without Stockbridge damperwas performed using commercial software SAP2000 A sinesweep wave was used to investigate the control effects onthe piping system under wide frequency range In order toconfirm the control effects of the Stockbridge damper underrandom earthquake vibration the three selective (El CentroCalifornia and Northridge) earthquakes were used in thisinvestigation

2 Piping System

21 Outline of Piping System The nuclear power plant pipingsystem was composed of 2- and 3-inch sized pipes the lengthof the axis of ordinates is 178m the end of the pipe tip wasfixed and 2 reducers were modeled as hinge conditions It isassumed that the inner space of the pipe was filled with waterThe water was modeled as an additional mass

Table 1 Material properties

Item Value UnitYoungrsquos modulus 199000 MPaPoissonrsquos ratio 031 mdashSteel density 7850 kgm3

Water density 1000 kgm3

Table 2 Section properties

Pipe size(in)

External diameter(mm)

Internal diameter(mm)

Thickness(mm)

2 603 428 8743 889 666 1113

Figure 1 shows the piping system modeled by SAP2000The material properties and cross-sectional properties of thepipe are shown in Tables 1 and 2 All properties were appliedas the values suggested by the design criteria

22 Free Vibration Analysis A free vibration analysis wasperformed with respect to the piping system in order tocalculate the parameters of the damper such as mass fre-quency ratio and damping ratio From the free vibrationanalysis the first to third modes show very complex modalshapes which are a combination of horizontal and verticalshapes as shown in Figures 2ndash4 The first and third modeshapes are predominantly horizontal mode shaped and thesecond mode shape is predominantly vertical mode shapedThe maximum amplitudes of where the damping device willbe installed were marked using a red color dot The dynamicproperties of the piping system calculated from free vibrationanalysis results are shown in Table 3

Since the main control target modes are the first to thirdmodes each generalized mass was calculated up to the thirdmode




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3 Design of Dampers




(1)


Mass

Messenger cable


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119872 + 119862 + 119870119909 = 0 (2)



1205961 = (ℎ minus 1198862119898120588 )12

1205962 = (ℎ + 1198862119898120588 )12


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RMS = radic 1119873119873sum119899=1

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Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















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(a) Plane view

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(a) Plane view

XY

Z

(b) Elevation view


3 Design of Dampers




(1)


Mass

Messenger cable


Connection part

Piping system

Z

X





119872 + 119862 + 119870119909 = 0 (2)



1205961 = (ℎ minus 1198862119898120588 )12

1205962 = (ℎ + 1198862119898120588 )12


(3)





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RMS = radic 1119873119873sum119899=1

1003816100381610038161003816acc11989910038161003816100381610038162 (4)




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Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Mass

Messenger cable


Connection part

Piping system

Z

X





119872 + 119862 + 119870119909 = 0 (2)



1205961 = (ℎ minus 1198862119898120588 )12

1205962 = (ℎ + 1198862119898120588 )12


(3)





4 Base Excitation




0 5 10 15 20 25 30 35 40 45 50Time (sec)

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El Centro x-dir

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El Centro z-dir

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RMS = radic 1119873119873sum119899=1

1003816100381610038161003816acc11989910038161003816100381610038162 (4)




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Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

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0 5 10 15 20 25 30 35 40 45 50Time (sec)

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02

El Centro z-dir

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Northridge y-dir

0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

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Northridge z-dir

Acc

(ms

ec2)

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(ms

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minus4

minus2

minus4

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Acc

(ms2)






RMS = radic 1119873119873sum119899=1

1003816100381610038161003816acc11989910038161003816100381610038162 (4)




Time (sec)


10

5

0

minus5

minus10

1009080706050403020100

Acc

(ms

ec2)


Frequency (Hz)


100

101

10minus1

0

10

20

30

40

Acc

(ms2)



Time (sec)


1009080706050403020100

0

2

4

Acc

(ms

ec2)

minus4

minus2


Frequency (Hz)


100

101

10minus1

0

5

10

15

20

Acc

(ms2)



Time (sec)


1009080706050403020100

Acc

(ms

ec2)

10

5

0

minus5

minus10


Frequency (Hz)


100

101

10minus1

0

10

20

30

40

50

Acc

(ms2)




Time (sec)


1009080706050403020100

Acc

(ms

ec2)

0

2

4

minus4

minus2



10

15

20

5

0

100

101

10minus1

Acc

(ms2)



Frequency (Hz)



100

101

10minus10 5 10 15 20 25 30 35 40 45 50

Time (sec)

0

1

2

minus1

minus2

Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10

Acc

(ms

ec2)



0

10

20

30

40

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4

Acc

(ms

ec2)



0

5

10

15

Acc

(ms2)




0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

1

2

3

Frequency (Hz)

0

2

4

6

8

10

100

101

10minus1

minus1

minus2

minus3



Acc

(ms

ec2)

Acc

(ms2)














Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10



Acc

(ms

ec2)

0

10

20

30

40

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)







0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

2

4


010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)



0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

1

2


010

110

minus1

minus1

minus2



Acc

(ms

ec2)

0

2

4

6

8

10

Acc

(ms2)










Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

1

2

California y-dir

0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

1

2

California z-dir

Acc

(ms

ec2)

Acc

(ms

ec2)

minus2

minus1

minus2

minus1


Frequency (Hz)

y-dirz-dir

100

101

10minus1

0

1

2

3

4

5

6

Acc

(ms2)



0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Northridge y-dir

0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Northridge z-dir

Acc

(ms

ec2)

Acc

(ms

ec2)

minus4

minus2

minus4

minus2


Frequency (Hz)

y-dirz-dir

100

101

10minus1

0

1

2

3

4

5

6

7

8

9

10

Acc

(ms2)






RMS = radic 1119873119873sum119899=1

1003816100381610038161003816acc11989910038161003816100381610038162 (4)




Time (sec)


10

5

0

minus5

minus10

1009080706050403020100

Acc

(ms

ec2)


Frequency (Hz)


100

101

10minus1

0

10

20

30

40

Acc

(ms2)



Time (sec)


1009080706050403020100

0

2

4

Acc

(ms

ec2)

minus4

minus2


Frequency (Hz)


100

101

10minus1

0

5

10

15

20

Acc

(ms2)



Time (sec)


1009080706050403020100

Acc

(ms

ec2)

10

5

0

minus5

minus10


Frequency (Hz)


100

101

10minus1

0

10

20

30

40

50

Acc

(ms2)




Time (sec)


1009080706050403020100

Acc

(ms

ec2)

0

2

4

minus4

minus2



10

15

20

5

0

100

101

10minus1

Acc

(ms2)



Frequency (Hz)



100

101

10minus10 5 10 15 20 25 30 35 40 45 50

Time (sec)

0

1

2

minus1

minus2

Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10

Acc

(ms

ec2)



0

10

20

30

40

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4

Acc

(ms

ec2)



0

5

10

15

Acc

(ms2)




0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

1

2

3

Frequency (Hz)

0

2

4

6

8

10

100

101

10minus1

minus1

minus2

minus3



Acc

(ms

ec2)

Acc

(ms2)














Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10



Acc

(ms

ec2)

0

10

20

30

40

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)







0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

2

4


010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)



0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

1

2


010

110

minus1

minus1

minus2



Acc

(ms

ec2)

0

2

4

6

8

10

Acc

(ms2)










Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















Time (sec)


10

5

0

minus5

minus10

1009080706050403020100

Acc

(ms

ec2)


Frequency (Hz)


100

101

10minus1

0

10

20

30

40

Acc

(ms2)



Time (sec)


1009080706050403020100

0

2

4

Acc

(ms

ec2)

minus4

minus2


Frequency (Hz)


100

101

10minus1

0

5

10

15

20

Acc

(ms2)



Time (sec)


1009080706050403020100

Acc

(ms

ec2)

10

5

0

minus5

minus10


Frequency (Hz)


100

101

10minus1

0

10

20

30

40

50

Acc

(ms2)




Time (sec)


1009080706050403020100

Acc

(ms

ec2)

0

2

4

minus4

minus2



10

15

20

5

0

100

101

10minus1

Acc

(ms2)



Frequency (Hz)



100

101

10minus10 5 10 15 20 25 30 35 40 45 50

Time (sec)

0

1

2

minus1

minus2

Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10

Acc

(ms

ec2)



0

10

20

30

40

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4

Acc

(ms

ec2)



0

5

10

15

Acc

(ms2)




0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

1

2

3

Frequency (Hz)

0

2

4

6

8

10

100

101

10minus1

minus1

minus2

minus3



Acc

(ms

ec2)

Acc

(ms2)














Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10



Acc

(ms

ec2)

0

10

20

30

40

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)







0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

2

4


010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)



0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

1

2


010

110

minus1

minus1

minus2



Acc

(ms

ec2)

0

2

4

6

8

10

Acc

(ms2)










Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Time (sec)


1009080706050403020100

Acc

(ms

ec2)

0

2

4

minus4

minus2



10

15

20

5

0

100

101

10minus1

Acc

(ms2)



Frequency (Hz)



100

101

10minus10 5 10 15 20 25 30 35 40 45 50

Time (sec)

0

1

2

minus1

minus2

Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10

Acc

(ms

ec2)



0

10

20

30

40

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4

Acc

(ms

ec2)



0

5

10

15

Acc

(ms2)




0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

1

2

3

Frequency (Hz)

0

2

4

6

8

10

100

101

10minus1

minus1

minus2

minus3



Acc

(ms

ec2)

Acc

(ms2)














Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10



Acc

(ms

ec2)

0

10

20

30

40

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)







0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

2

4


010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)



0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

1

2


010

110

minus1

minus1

minus2



Acc

(ms

ec2)

0

2

4

6

8

10

Acc

(ms2)










Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 5 10 15 20 25 30 35 40 45 50Time (sec)

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

1

2

3

Frequency (Hz)

0

2

4

6

8

10

100

101

10minus1

minus1

minus2

minus3



Acc

(ms

ec2)

Acc

(ms2)














Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10



Acc

(ms

ec2)

0

10

20

30

40

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)







0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

2

4


010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)



0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

1

2


010

110

minus1

minus1

minus2



Acc

(ms

ec2)

0

2

4

6

8

10

Acc

(ms2)










Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

5

10

Frequency (Hz)10

010

110

minus1

minus5

minus10



Acc

(ms

ec2)

0

10

20

30

40

Acc

(ms2)


Time (sec)0 5 10 15 20 25 30 35 40 45 50

0

2

4

Frequency (Hz)10

010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)







0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

2

4


010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)



0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

1

2


010

110

minus1

minus1

minus2



Acc

(ms

ec2)

0

2

4

6

8

10

Acc

(ms2)










Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

2

4


010

110

minus1

minus2

minus4



Acc

(ms

ec2)

0

5

10

15

20

Acc

(ms2)



0 5 10 15 20 25 30 35 40 45 50

0

05

1


010

110

minus1

minus05

minus1



Acc

(ms

ec2)

0

1

2

3

4

5

Acc

(ms2)


0 5 10 15 20 25 30 35 40 45 50

0

1

2


010

110

minus1

minus1

minus2



Acc

(ms

ec2)

0

2

4

6

8

10

Acc

(ms2)










Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of
























Competing Interests


Acknowledgments


References






















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















Documents

Research Article Vibration Control of Nuclear Power Plant ...downloads.hindawi.com/journals/stni/2016/5014093.pdf · Research Article Vibration Control of Nuclear Power Plant Piping