International Journal of Vehicle Noise and Vibration

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Int. J. Vehicle Noise and Vibration, Vol. 4, No. 1, 2008 35

Copyright 2008 Inderscience Enterprises Ltd.

Vibro-acoustic analysis of composite circular discwith various orthotropic properties under thermalenvironment

Boorle Rajesh Kumar, N. Ganesan*and Raju Sethuraman

Machine Design Section, Department of Mechanical Engineering,

Indian Institute of Technology Madras, Chennai-600036, India

Fax: +91 44 2350509

E-mail: [email protected]



*Corresponding author

Abstract: Composite circular discs with polar orthotropic and rectangularorthotropic fibres of different composite materials are modelled and theirvibration response due to harmonic point load under thermal environment wascomputed by Finite Element Method (FEM) using ANSYS. Acoustic responseof composite circular disc was computed by coupling the vibration data fromFEM to the Boundary Element Method (BEM) using LMS SYSNOISE.

Keywords: finite element method; FEM; boundary element method; BEM;critical buckling temperature; commercial CAE packages ANSYS and LMSVIRTUAL LAB with LMS SYSNOISE as solver.

Reference to this paper should be made as follows: Rajesh Kumar, B.,Ganesan, N. and Sethuraman, R. (2008) Vibro-acoustic analysis of compositecircular disc with various orthotropic properties under thermal environment,Int. J. Vehicle Noise and Vibration, Vol. 4, No. 1, pp.3569.

Biographical notes: Boorle Rajesh Kumar is currently research scholar inIndian Institute of Technology Madras, doing research in the area ofvibro-acoustic analysis of Composite and FGM structures under thermalenvironment. He received undergraduate degree in mechanical engineeringfrom Nagarjuna university and yet to receive post graduate degree from IndianInstitute of Technology at Madras.

N. Ganesan is currently Professor in Indian Institute of Technology Madras.His on going research is in the areas of vibro-acoustic analysis of Composite

and FGM structures, under thermal environment and Active vibration controlusing smart materials. He is the author of more than 200 papers in the openliterature. He received his PhD Degree in 1975 from Indian Institute ofTechnology at Madras.

Raju Sethuraman is currently Professor in Indian Institute of TechnologyMadras. His on going research is in the areas of fracture and fatigue analysis ofengineering structures. He received his PhD Degree in 1990 from IndianInstitute of Technology at Bombay.


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36 B. Rajesh Kumar et al.

1 Introduction

Circular discs are widely used in mechanical components like rotors, fly wheels,

clutches, brakes mounted on power transmission shafts, transducers in defense

applications and hydrophones in sensing applications. Now a days in designing

components for applications like aerospace, light vehicles and automobiles weight is the

primary concern. Composite materials which are of high stiffness to mass ratio with polar

orthotropic composites of fibre angle = 0, = 90 and rectangular orthotropiccomposites are used in many of above applications. These composite circular discs

vibrate and radiate sound when subjected to several types of loadings during their

application. They behave peculiar when subjected to thermal environment.

There is a substantial amount of literature available on buckling and modal analysis

of circular disc. Vogel and Skinner (1965) investigated natural frequencies of a uniform

annular disc; Thompson (1971) computed self and mutual radiation impedances of auniformly vibrating annular or circular piston by integration of the far-field directivity

function. Wang and Thevendran (1993) used the Raleigh-Ritz method, based on the thin

plate theory, Lee and Singh (1994) presented analytical formulations for annular disc

sound radiation using structural modes. Raveendra et al. (1998) and Vlahopoulos and

Raveendra (1998) used indirect Boundary Element Method (BEM) for structural

acoustics, von Estorff and Zaleski (2003) and Wu (2005) also used Boundary Element

Method (BEM) for prediction of structural acoustics. Qatu (2004) also conducted studies

on vibrations of laminated shells and plates. Lee and Singh (2005a, 2005b) proposed a

polynomial approximation for modal acoustic power radiation from a thin annular disc.

From the literature it is found that the studies on vibro-acoustic behaviour of

composite circular disc under thermal environment have not been attempted. This work is

an extension of our previous work without thermal effect (accepted for publication) and

here we concentrated our study on vibration and acoustic analysis of composite circular

disc subjected to harmonic point load under thermal environment i.e., by considering pre-

stress effect and thermal loading is expected from the fluid domain surrounding the

vibrating structure of temperature independent material properties.

In general vibration response of the structure is computed by Finite Element Method

(FEM) and acoustic response is computed by BEM while using FEM for acoustic

analysis infinite domain has to be meshed which demands high computation time.

Generally for computing vibro-acoustic response FEM and BEM are coupled to take

advantage of both the methods. In the present work, commercial CAE tools ANSYS is

used to compute vibration response and LMS SYSNOISE is used to compute sound

radiation from the vibrating composite circular disc.

2 Methodology used

In the present section the methodology of the approach is presented. The geometrical

characteristic of circular disc, details of FE and BE meshes for both the vibration and

acoustic analysis cases are explained.


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Vibro-acoustic analysis of composite circular disc under thermal environment 37

2.1 Dimensions of circular disc used for vibro-acoustic analysis

The circular disc shown in Figure 1 used for vibro-acoustic analysis whose outer radius

R = 0.5 m, inner radius R0 = 0.25 m and thickness H= 0.01 m. The disc is fixed at both

the inner and outer radii and subjected to harmonic loading with unit amplitude at

different radial positions given in Figure 2 (0.0, 0.30, 0.0), (0.0, 0.375, 0.0) and

(0.0, 0.45, 0.0) the field points are created exactly 0.5 m above the application of

harmonic point load (0.0, 0.30, 0.50), (0.0, 0.375, 0.50) and (0.0, 0.45, 0.50) to measure

pressure level at that particular location and acceleration response is measured at point of

application of harmonic load.

Figure 1 Dimensions of circular disc

Figure 2 Circular disc subjected to harmonic loading at different radial positions and with fieldpoints in space exactly 0.5 m above the point of application of load

2.2 Finite Element Method (FEM) for vibration analysis

The mesh used in ANSYS for vibration analysis of all cases of circular disc is shown in

Figure 3 and shell181 is the assigned element type. In the applications like clutches,

brakes, fly wheels and rotors, thin plate theory is not valid hence in such cases elements

like shell181, shell91, shell93, and shell99 are to be used. These shell elements are based

on first order shear deformation theory (usually referred as Mindlin-Reissner plate

theory). So they are compatible for modelling composite structures with different fibre

orientations and different types of orthotropic by changing elemental coordinate system.

Structural damping can also be assigned, generally for composite structures damping is

more compared to structures made up of isotropic material. In current vibro-acoustic

analysis for all cases of composite circular discs it is assumed as 1%.


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Figure 3 Details of shell element and FE mesh used for vibration analysis: (a) ANSYS element

shell181 and (b) mesh used for vibration analysis (see online version for colours)

(a) (b)

2.3 Different types of orthotropic properties

In ANSYS while modelling orthotropic materials elemental coordinate system is

modified to global coordinate system. For the case of rectangular orthotropic

(Figure 4(a)) fibre orientation is along Cartesian coordinates so elemental coordinate

system is aligned with global Cartesian coordinate system. For polar orthotropic = 90

(Figure 4(b)) fibre orientation is along circumferential direction so elemental coordinate

system is aligned with global cylindrical coordinate system in circumferential direction.

For polar orthotropic = 0 (Figure 4(c)) fibre orientation along radial direction so

elemental coordinate system is aligned with global cylindrical coordinate system in radial

direction.

Figure 4 Different types of orthotropic properties used for vibro-acoustic analysis:(a) rectangular orthotropic; (b) circumferential orthotropic and (c) radial orthotropic

(a) (b) (c)

Construction of rectangular orthotropic circular disc is easy among all cases due to its

simplicity; generally it is prepared by cutting rectangular composite plate. In the case of

circumferential and radial orthotropic circular disc orienting fibre along circumferential

and radial directions is a difficult task. In general orthotropic circular disc for different

boundary conditions has peculiar behaviour in strength point of view. In current study,

vibro-acoustic analysis of orthotropic circular disc is carried out for the fixed-fixed

boundary condition.


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2.4 Prediction of thermal loading by conducting thermal buckling analysis

In general, instability of structures under thermal environment is considered as serious

effect because thermal load required for thermal buckling is much less than the

mechanical load required for mechanical buckling and mechanical forces induced on

structures during application are much less than the mechanical buckling load.

In ANSYS buckling analysis is conducted by two ways linear and non linear eigen-value

buckling.

For the current study, linear eigen-value buckling analysis is conducted to find

bifurcation point where structures are supposed to buckle. Initial stress stiffening effect

induced on structure due to buckling load is calculated by conducting static analysis with

pre-stress effect on. After conducting thermal buckling analysis thermal loads to be

applied on the structure is decisive as fractions of thermal buckling load so 0.0 (no

thermal effect) 0.25, 0.50, 0.75, 0.95 (near to thermal buckling load) are considered asthermal loads.

([ ] [ ]){ } {0}i iK S + =

[K]is the stiffness matrix, [S]is the stress stiffening and iis the eigen vector.The critical buckling temperature of composite circular discs with various orthotropic

for the fixed-fixed boundary condition given in Table 1, among all cases radial

orthotropic has more critical buckling temperature.

Table 1 Critical buckling temperatures (C) when different materials used

Composite material Rectangular Circumferential Radial

Graphite-epoxy 293 235 967

Boron-epoxy 172 166 431

Glass-epoxy 252 240 501

2.5 Prediction of vibration response under thermal environment

When structures subjected to thermal loading then stress stiffening effect takes place

which leads to change in natural frequencies and shift of frequency response curves, this

effect is induced by conducting initial static analysis with pre-stress effect on. The block

diagram for vibro-acoustic analysis of composite circular disc under thermal environment

is given in Figure 5.

Figure 5 Block diagram of vibro-acoustic analysis of composite circular subjected to point

excitation under thermal loads


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3 Boundary Element Method (BEM) for acoustic analysis

BEM involves creation of boundary element mesh along surface of the structure and field

points in interior and exterior domains. Computing frequency dependant BEM influence

matrices, specifying solvers like Direct BEM or In Direct BEM. Incorporate boundary

conditions like mentioning interior or exterior in the case of Direct BEM, free edges

where jump across surface is zero in the case of IBEM. Generally for computing acoustic

response, In Direct BEM is used because sound radiation is computed on both sides of

boundary element mesh i.e., interior and exterior domains of boundary. The boundary

element mesh is created along the surface of the structure by using finite element mesh

used for vibration analysis but in general FE meshes are highly dense and consist of

interior nodes and elements, in such cases FE mesh is converted to BE mesh by

coarsening and skinning the structural FE mesh using LMS VIRTUAL LAB

pre acoustics. But in present case the skinning operation is not required because the FEmesh does not have any interior nodes or elements, so directly the FE mesh file employed

for vibration analysis in ANSYS is employed for acoustic analysis in LMS SYSNOISE

and displacements from ANSYS are imported on BE mesh (Figure 6(a)) without any

interpolation by using .rst1 which consists of FE results like displacements, stresses and

strain. The boundary conditions of free edges are imposed for circular disc at inner and

outer periphery given in Figure 6(b). After importing displacements on BE mesh primary

variables like velocities and pressures are calculated for BE mesh and secondary results

at field points are processed.

Figure 6 Details of BE mesh and free edges specified on composite circular disc used foracoustic analysis in LMS SYSNOISE: (a) BE-mesh used for acoustic analysis in LMSSYSNOISE and (b) free edges specified on the inner and outer edges of circular disc

(see online version for colours)

(a) (b)

4 Vibro-acoustic response of graphite epoxy circular disc with variousorthotropic subjected to point excitation at different radial positions

4.1 Rectangular orthotropic

The driven point admittance for composite circular disc with rectangular orthotropic is

calculated at different radial positions to predict position where point excitation has more

influence on vibration and sound radiation of structure. From Figure 7 it is observed it is

more for radial position 0.375m, also the same for acceleration response (Figure 8).


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For rectangular orthotropic both radial and circumferential modes are coupled so

point excitation leads to excitation of both radial and circumferential modes. From thevibro-acoustic response of graphite-epoxy circular disc with rectangular orthotropic,

subjected to point excitation at different radial positions it is evident, point excitation at

radial position 0.375 m has more influence on vibro-acoustic behaviour also radiated

sound pressure and power level are more, from Figures 9 and 10 respectively.

Figure 7 Driven point admittance from circular disc with rectangular orthotropic(see online version for colours)

Figure 8 Acceleration response from composite circular disc with rectangular orthotropicsubjected to point excitation at different radial positions (see online version for colours)


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Figure 9 Radiated sound pressure from composite circular disc with rectangular orthotropic

subjected to point excitation at different radial positions (see online version for colours)

Figure 10 Radiated sound power level from composite circular disc with rectangular orthotropicsubjected to point excitation at different radial positions (see online versionfor colours)

4.2 Circumferential orthotropic

The vibro-acoustic response of graphite-epoxy circular disc with circumferential

orthotropic and excited with point excitation at different radial positions is given in

Figures 1114, at the position of 0.375 m maximum number of modes for a circular disc


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are excited and radiate sound, from driven point admittance (Figure 11) point excitation

at that radial position has more influence on vibration and sound radiation of structure.Also the radiated sound power level from Figure 13 was greater for the radial position

of 0.375 m. So further study is carried out with point excitation at this radial position.

Figure 11 Driven point admittance from circular disc with circumferential orthotropic(see online version for colours)

Figure 12 Acceleration response from composite circular disc with circumferential orthotropic

subjected to point excitation at different radial positions (see online version forcolours)


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Figure 13 Radiated sound pressure from composite circular disc with circumferential

orthotropic subjected to point excitation at different radial positions (see onlineversion for colours)

Figure 14 Radiated sound power level from composite circular disc with circumferentialorthotropic subjected to point excitation at different radial positions (see onlineversion for colours)

4.3 Radial orthotropic

The vibro-acoustic response of graphite-epoxy circular disc with radial orthotropic and

excited with point excitation at different radial positions is given in Figures 1518.

In the case of radial orthotropic all modes of circular disc are excited and radiate sound at


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all positions of point excitation, but at the position of 0.375 m all modes of a circular

disc are excited. Driven point admittance, radiated sound pressure and power level(Figures 1618) shows point excitation at that radial position has more influence on

vibration and sound radiation of structure.

Figure 15 Driven point admittance from circular disc with radial orthotropic (see online versionfor colours)

Figure 16 Acceleration response from composite circular disc with radial orthotropic subjectedto point excitation at different radial positions (see online version for colours)


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Figure 17 Radiated sound pressure from composite circular disc with radial orthotropic

subjected to mechanical excitation at different radial positions (see online versionfor colours)

Figure 18 Radiated sound power level from composite circular disc with radial orthotropicsubjected to mechanical excitation at different radial positions (see online versionfor colours)

4.4 Analysis of mode shapes of graphite epoxy circular disc with variousorthotropic

Mode shapes of rectangular, circumferential and radial orthotropic circular disc are given

in Figure 19(a)(c) respectively. In the case of circumferential, radial orthotropic

antinodes exist at the position (0, 0.375 m, 0) so that maximum number of modes are


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excited and radiate sound when the point excitation is at that location and for rectangular

orthotropic anti nodes are near to that location. Further study on different materials iscarried out with point excitation at that position.

Figure 19 Mode shapes of graphite epoxy circular disc with various orthotropic:(a) rectangular orthotropic circular disc; (b) circumferential orthotropic circular discand (c) radial orthotropic circular disc (see online version for colours)

(a)

(b)

(c)

5 Vibro-acoustic analysis of graphite epoxy circular disc with various

orthotropic subjected to point excitation under thermal environment

5.1 Rectangular orthotropic

The displacement, velocity and acceleration plots for rectangular orthotropic circular disc

for different thermal loadings are given in Figures 2022 respectively, as temperature

increases huge shift in frequencies occurs at last fundamental mode reaches to zero when

temperature is increased to critical buckling temperature i.e., zone of instability of a

structure.


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There is an increase in displacements and velocities as thermal load increases but

decrease in acceleration because of low operating frequency range. Radiated soundpressure level (Figure 23) at the field point 0.50 m above of point of application of load is

decreasing as thermal load increases because it is dependant on velocity, acceleration and

operating frequency range of the vibrating structure.

Figure 20 Normal displacements of circular disc with rectangular orthotropic under increasingthermal load (see online version for colours)

Figure 21 Normal velocities of circular disc with rectangular orthotropic under increasingthermal load (see online version for colours)


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Figure 22 Acceleration response from circular disc with rectangular orthotropic under

increasing thermal load (see online version for colours)

Figure 23 Radiated sound pressure from circular disc with rectangular orthotropic underincreasing thermal load (see online version for colours)

Radiated sound power level (Figure 24) which signifies sound power generated by

vibrating structure transmitted to surrounding environment, remains same at all thermal

loadings for circular disc with rectangular orthotropic. Radiation efficiency Figure 25


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which is the ratio of radiated sound power to vibrational energy of the structure, is more

than one i.e. radiated sound power is more than the vibrational energy, and it isdecreasing as thermal loading increases.

Figure 24 Radiated sound power level from circular disc with rectangular orthotropic underincreasing thermal load (see online version for colours)

Figure 25 Radiation efficiency of circular disc with rectangular orthotropic under increasingthermal load (see online version for colours)


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Directivity pattern of radius 0.375 m at 0.50 m above the vibrating circular disc for three

modes are given in Figure 26 they indicate the occurrence of maximum pressure at anyother point in dir. For the fixed-fixed boundary condition more number of ripplesobserved in the dir for second and third modes.

Figure 26 Directivity pattern for three modes of circular disc with rectangular orthotropic underincreasing thermal load: (a) position at which directivity pattern is measured;(b) Mode 1; (c) Mode 2 and (d) Mode 3 (see online version for colours)

(a)

(b)


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Figure 26 Directivity pattern for three modes of circular disc with rectangular orthotropic under

increasing thermal load: (a) position at which directivity pattern is measured;(b) Mode 1; (c) Mode 2 and (d) Mode 3 (see online version for colours) (continued)

(c)

(d)

5.2 Circumferential orthotropic

The displacement, velocity and acceleration plots for circumferential orthotropic

circular disc for different thermal loadings are given in Figures 2729 respectively,

as temperature increases huge shift in frequencies occurs at last fundamental mode


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reaches to zero when temperature is increased to critical buckling temperature i.e., zone

of instability of a structure.

Figure 27 Normal displacements of circular disc with circumferential orthotropic underincreasing thermal load (see online version for colours)

Figure 28 Normal velocities of circular disc with circumferential orthotropic under increasing

thermal load (see online version for colours)


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Figure 29 Acceleration response from circular disc with circumferential orthotropic under

increasing thermal load (see online version for colours)


decrease in acceleration from 0.50 times critical buckling temperature to critical

buckling temperature because of low operating frequency range. Radiated sound pressure

level (Figure 30) at the field point 0.50 m above of point of application of load is

decreasing as thermal load increases because it is dependant on the velocity, acceleration

and operating frequency range of the vibrating structure.

Figure 30 Acoustic response from circular disc with circumferential orthotropic underincreasing thermal load (see online version for colours)


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vibrating structure transmitted to surrounding environment, increases as thermal loadingincreases for circular disc with circumferential orthotropic. Radiation efficiency

(Figure 32) which is the ratio of radiated sound power to vibrational energy of the

structure, is more than one i.e., radiated sound power is more than the vibrational energy,

and it is decreasing as thermal loading increases.

Figure 31 Radiated sound power level from circular disc with circumferential orthotropic underincreasing thermal load (see online version for colours)

Figure 32 Radiation efficiency of circular disc with circumferential orthotropic underincreasing thermal load (see online version for colours)


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modes are given in Figure 33 they indicate the occurrence of maximum pressure at anyother point in dir. For the fixed-fixed boundary condition more number of ripplesobserved in the dir for second and third modes.

Figure 33 Directivity pattern for three modes of circular disc with circumferential orthotropicunder increasing thermal load: (a) position at which directivity pattern is measured;(b) Mode 1; (c) Mode 2 and Mode 3 (see online version for colours)

(a)

(b)


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Figure 33 Directivity pattern for three modes of circular disc with circumferential orthotropic

under increasing thermal load: (a) position at which directivity pattern is measured;(b) Mode 1; (c) Mode 2 and Mode 3 (see online version for colours) (continued)

(c)

(d)

5.3 Radial orthotropic

Generally composites can not sustain temperatures above 250C because epoxy resins

burn at those temperatures. In current case of radial orthotropic thermal loadings on the

circular disc are restricted up to 250C, vibration response is found at 0, 100, 200 and

250C. The displacement, velocity and acceleration plots for radial orthotropic circular


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disc for different thermal loadings are given in Figures 3436 respectively,

as temperature increases there is a considerable shift in frequencies.

Figure 34 Normal displacements of a circular disc with radial orthotropic under increasingthermal load (see online version for colours)

Figure 35 Normal velocities of a circular disc with radial orthotropic under increasingthermal load (see online version for colours)


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Figure 36 Acceleration response from circular disc with radial orthotropic under increasing

thermal load (see online version for colours)

Figure 37 Radiated sound pressure level from circular disc with radial orthotropic underincreasing (see online version for colours)


decrease in acceleration from 250C, because of low operating frequency range as

thermal load increases. Similar trend is observed in the case of acceleration and radiated

sound pressure levels (Figure 37).


vibrating structure transmitted to surrounding environment, increases as thermal loading

increases for circular disc with radial orthotropic. Radiation efficiency (Figure 39) which


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is the ratio of radiated sound power to vibrational energy of the structure, is more than

one i.e., radiated sound power is more than the vibrational energy and it is increasing asthermal loading increases up to 200C with a sudden decrease at 250C.

Figure 38 Radiated power level from circular disc with radial orthotropic under increasingthermal load (see online version for colours)

Figure 39 Radiation efficiency of circular disc with radial orthotropic under increasing thermal

load (see online version for colours)


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modes under increasing thermal loading up to critical buckling temperature given inFigure 40 for the sake of finding the sound wave generated from the circular disc with

radial orthotropic though existence of disc is difficult at those high temperatures, they

indicate the occurrence of maximum pressure at any other point in dir.For the fixed-fixed boundary condition more number of ripples observed in the

dir for second and third modes. Peculiar observation was made by directivity pattern(Figure 40) for the circular disc with radial orthotropic, when thermal loading is near to

critical buckling temperature the directivity pattern got squeezed for all modes.

Figure 40 Directivity pattern for three modes of circular disc with radial orthotropic underincreasing thermal load: (a) position at which directivity pattern is measured;(b) Mode 1; (b) Mode 2 and (c) Mode 3 (see online version for colours)

(a)

(b)


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Figure 40 Directivity pattern for three modes of circular disc with radial orthotropic under

increasing thermal load: (a) position at which directivity pattern is measured;(b) Mode 1; (c) Mode 2 and (d) Mode 3 (see online version for colours) (continued)

(c)

(d)

6 Inferences from displacements and velocities on radiated sound pressure

Natural frequencies, displacements and velocities of graphite epoxy circular disc with all

cases of orthotropic with out thermal effect are tabulated in Table 2 and acceleration,

sound pressure level are tabulated in Table 3. It is evident from Tables 2 and 3 when


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vibrating structures displacements and velocities are high then sound radiated from the

vibrating structure will also be high. For the case of rectangular orthotropicdisplacements and velocities are high at first and second modes hence sound radiation is

also more among other orthotropic properties, from third mode sound radiation is more

for circumferential orthotropic because displacements are high among other orthotropic.

Table 2 Natural frequency, displacement and velocity of circular disc with various orthotropic

Natural frequency (Hz) Displacements (m) Velocity (m/s)

Rect. Circum. Radial Rect. Circum. Radial Rect. Circum. Radial

500 430 1450 10.6e6 4.01E6 1.54e6 0.03331 0.01084 0.01404

950 465 1500 1.14e6 2.58E6 0.69e6 0.00775 0.00754 0.00655

1240 555 1555 0.28e6 2.24E6 0.72e6 0.00218 0.00781 0.00683

Table 3 Natural frequency, acceleration and radiated sound pressure levels of circular discwith various orthotropic

Natural frequency (Hz)Acceleration

(dB re 20e6 m/s2)Radiated sound pressure

(dB re 20e6 Pa)

Rect. Circum. Radial Rect. Circum. Radial Rect. Circum. Radial

500 430 1450 135.3 123.3 136.5 101.8 93.6 97.6

950 465 1500 127.2 123.3 130.1 94.2 87.9 90.6

1240 555 1555 118.0 122.7 128.1 84.5 85.5 85.3

Under thermal environment even though displacements and velocities (Table 4) areincreasing as thermal load increases to critical buckling temperature, acceleration level

(Table 5) is decreasing in the case of rectangular orthotropic but for circumferential and

radial orthotropic it is increasing up to 0.250.50 times critical buckling temperature and

decreasing for further increase, for all cases radiated sound pressure level is decreasing

due to huge shift in frequencies.

Table 4 Natural frequency, displacement and velocity for first mode of circular disc withvarious orthotropic under increasing thermal load

Natural frequency (Hz) Displacements (m) Velocity (m/s)Thermal loadingref to Tcr(C) Rect. Circum. Rect. Circum. Rect. Circum.

0.0 Tcr 500 430 1.1E5 4.0E6 0.0370 0.01082

0.25 Tcr 430 380 1.3E5 5.3E6 0.0362 0.01267

0.50 Tcr 360 310 1.7E5 9.3E6 0.0400 0.01825

0.75 Tcr 250 220 2.7E5 1.2E5 0.0426 0.01779

0.95 Tcr 110 108 1.0E4 6.8E5 0.0735 0.04669


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Table 5 Natural frequency, acceleration and radiated sound pressure for first mode of circular

disc with various orthotropic under increasing thermal load

Natural frequency (Hz)Acceleration

(dB re 20e6 m/s2)adiated sound pressure

(dB re 20e6 Pa)Thermal loadingref to Tcr(C) Rect. Circum Rect. Circum Rect. Circum

0.0 Tcr 500 430 135.3 123.3 101.8 93.6

0.25 Tcr 430 380 133.8 123.6 99.0 93.8

0.50 Tcr 360 310 133.2 125.0 97.0 90.4

0.75 Tcr 250 220 130.50 121.8 91.2 84.1

0.95 Tcr 110 108 128.1 124.0 81.3 82.3

7 Vibro-acoustic analysis of composite circular disc with variousorthotropic and different materials

Vibro-acoustic behaviour of different composite circular discs with temperature

independent material properties given in Table 6, for various orthotropic properties under

increasing thermal load up to critical thermal buckling temperature are tabulated in

Tables 712. Among all cases of orthotropic radial orthotropic has more strength and

circumferential orthotropic is having less strength, but in all cases of orthotropic as

thermal load increases shift of frequency is observed and finally reaches to zero when

thermal load is equal to critical buckling temperature i.e., zone of instability of a

structure.

Table 6 Material properties of composite for analysis

Composite material E1(GPa) E2 (GPa) v12 (kg/m3) (106/C) 2(10

6/C)

Graphite-epoxy 137.0 8.9 0.28 1600 0.50 27.4

Boron-epoxy 204.0 18.3 0.23 2000 6.1 30.3

Glass-epoxy 38.6 8.3 0.26 1810 6.3 20.50

Boron-epoxy

Table 7 Vibro-acoustic response of boron-epoxy circular disc with rectangular orthotropic

Natural frequency (Hz)

Acceleration

(dB re 20e6 m/s2)

Radiated sound pressure

(dB re 20e6 Pa)

0.0 0.25 0.50 0.75 0.95 0.0 0.25 0.50 0.75 0.95 0.0 0.25 0.50 0.75 0.95

575 500 410 290 125 133.7 132.4 131.6 130.2 133.7 101.7 99.3 97.6 92.0 88.2

1000 940 850 760 680 124.5 124.4 123.2 123.8 122.7 93.1 92.1 92.3 92.6 90.8

1325 1250 1180 1090 1020 120.0 120.0 119.5 120.0 118.0 84.8 85.6 86.0 86.7 86.7


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Table 8 Vibro-acoustic response of boron-epoxy circular disc with circumferential orthotropic


Acceleration

(dB re 20e6 m/s2)


(dB re 20e6 Pa)

0.0 0.25 0.50 0.75 0.95 0.0 0.25 0.50 0.75 0.95 0.0 0.25 0.50 0.75 0.95

530 470 390 280 120 123.4 125.8 126.0 122.0 121.2 94.0 96.7 96.3 81.2 58.8

555 485 410 300 160 122.7 124.0 124.8 122.0 121.3 90.9 88.8 94.8 90.7 59.7

630 545 450 330 190 121.4 122.2 120.50 121.6 121.4 86.2 81.8 75.6 77.3 82.9

Glass-epoxy

Table 9 Vibro-acoustic response of glass-epoxy circular disc with rectangular orthotropic


Acceleration

(dB re 20e6 m/s2)


(dB re 20e6 Pa)

0.0 0.25 0.50 0.75 0.95 0.0 0.25 0.50 0.75 0.95 0.0 0.25 0.50 0.75 0.95

400 345 285 205 95 132.7 134.5 135.0 133.3 131.1 97.6 98.5 96.3 90.7 82.3

590 535 475 410 340 125.7 126.0 124.8 125.0 124.5 92.3 93.0 92.2 90.6 88.0

740 690 640 585 530 117.8 120.0 118.4 117.4 117.7 84.9 88.9 90.50 89.7 89.0

Table 10 Vibro-acoustic response of glass-epoxy circular disc with circumferential orthotropic


Acceleration

(dB re 20e6 m/s2)


(dB re 20e6 Pa)

0.0 0.25 0.50 0.75 0.95 0.0 0.25 0.50 0.75 0.95 0.0 0.25 0.50 0.75 0.95

370 325 270 197 90 124.2 125.5 127.2 125.0 122.7 92.3 91.9 92.7 82.8 66.3

390 340 276 201 97 123.4 123.3 125.8 122.5 122.4 83.2 82.3 86.5 88.4 58.4

430 370 305 215 117 122.5 122.8 123.5 124.5 122.8 70.1 70.4 71.4 76.8 78.5

8 RMS values of radiated sound pressure (dB re 20e6 Pa)for all materials

In general by root mean square value of sound pressure we can predict whether sound

radiated from structure has adverse effect on the surrounding environment. From current

study RMS value of radiated sound pressure for different thermal loads and composite

materials is made of use for better estimation of vibro-acoustic behaviour of composite

material for a range of temperatures. The RMS plot of sound pressure radiated by the

vibrating composite circular disc with various orthotropic made up of different materials;

at specified field point location up to the range of buckling temperatures of respective

material given in Figures 4143.


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Figure 41 RMS value of radiated sound pressure from circular disc with rectangular orthotropic

under increasing thermal loads (see online version for colours)

Figure 42 RMS value of radiated sound pressure from circular disc with circumferentialorthotropic under increasing thermal loads (see online version for colours)


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Figure 43 RMS value of radiated sound pressure from circular disc with radial orthotropic under

increasing thermal loads (see online version for colours)

As temperature increases the RMS value is decreasing for the composite circular disc

with rectangular and circumferential orthotropic but in the case of radial orthotropic

circular disc it increases up to 0.50 times of critical buckling temperature and then after it

decreases. Among all materials boron epoxy is having low RMS value in all cases of

orthotropic and thermal loadings.

9 Conclusions

Critical observations from vibro-acoustic response of various orthotropic properties and

materials under thermal environment for fixed-fixed boundary condition

With out thermal loading

1 Driven point admittance is more for the point of excitation at radial position 0.375 m

and also radiated sound power, among remaining radial positions. So the point

excitation at radial position 0.375 has much influence on vibro-acoustic behaviour

of circular disc.

2 Among all cases of orthotropic circular discs, circular disc with circumferential

orthotropic is having low natural frequency and radial orthotropic is having highnatural frequency from Tables 2 and 3.

3 It is evident when displacements and velocities are high then sound radiated from the

vibrating structure will also be high without thermal effect (Tables 2 and 3). For the

case of rectangular orthotropic velocities are high at first and second modes hence

sound radiation is also high among other orthotropic properties at third mode sound

radiation is more for circumferential orthotropic because displacements are high

among other orthotropic properties. Similar observations are made from other

materials also.


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4 For radial orthotropic circular disc displacements at all modes are very less and

acceleration response at the point of force application is high due to high operatingfrequency range and in the case of other orthotropic circular disc displacements are

very high and acceleration response at the point of force application is low due to

low operating frequency range. Among all configurations radial orthotropic is stiffer

and similar trend is observed for other materials from Table 3.

5 Fundamental mode of circular disc with circumferential orthotropic is having low

pressure level and radial orthotropic is having high pressure level at mentioned field

point from Table 3 and similar trend is observed for other materials. In the remaining

modes circular disc with circumferential orthotropic is having high pressure level at

selected field point though there is low acceleration response from Table 3 at the

point of force application and radial orthotropic is having low pressure level at

mentioned field point though high acceleration response at the point of force

application

With thermal loading

6 Among all cases of orthotropic circumferential orthotropic is having low critical

buckling temperature and radial orthotropic is having high critical buckling

temperature from Table 1 and similar trend is observed for other materials.

Under thermal environment even though displacements and velocities are increasing

as thermal load increases to critical buckling temperature acceleration and radiated

sound pressure level are decreasing because of huge shift in frequencies.

7 The radiation efficiency from the vibrating and sound radiating circular disc with

clamped-clamped boundary conditions is more than one for all cases of orthotropic

properties under different thermal loadings i.e., radiated sound power in all cases of

circular disc is higher than vibrational energy. As thermal load increases radiation

efficiency is decreasing.

8 Directivity pattern of radius 0.375 m at 0.50 m above the circular disc for all modes

of graphite epoxy circular disc with various orthotropic under increasing thermal

load is given, more number of ripples are observed in dir for fixed-fixed

boundary conditions. Peculiar observation was made by directivity pattern

(Figure 40) for the circular disc with radial orthotropic, when thermal loading

is near to critical buckling temperature the directivity pattern got squeezed at all

modes.

9 As temperature increases the RMS value is decreasing for the composite circular disc

with rectangular and circumferential orthotropic but in the case of radial orthotropic

circular disc it increases up to 0.50 times of critical buckling temperature and thenafter it decreases. Among all materials boron epoxy is having low RMS value in all

cases of orthotropic and thermal loadings.

References

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Lee, H. and Singh, R. (2005a) Acoustic radiation from out-of-plane modes of an annular diskbased on thick plate theory,Journal of Sound and Vibration, Vol. 282, pp.313339.


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Note1Output file from ANSYS.

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