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Research Papers

Nonlinear Axisymmetric Free Vibration Analysis of Liquid-Filled Spherical Shell With Volume Constraint

[+] Author and Article Information
W. Jiammeepreecha

Department of Civil Engineering,
Faculty of Engineering and Architecture,
Rajamangala University of Technology Isan,
Nakhon Ratchasima 30000, Thailand
e-mail: weeraphan.ji@rmuti.ac.th

S. Chucheepsakul

Mem. ASME
Department of Civil Engineering,
Faculty of Engineering,
King Mongkut’s University of
Technology Thonburi,
Bangkok 10140, Thailand
e-mail: somchai.chu@kmutt.ac.th

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 17, 2016; final manuscript received April 6, 2017; published online July 13, 2017. Assoc. Editor: A. Srikantha Phani.

J. Vib. Acoust 139(5), 051016 (Jul 13, 2017) (13 pages) Paper No: VIB-16-1548; doi: 10.1115/1.4036500 History: Received November 17, 2016; Revised April 06, 2017

Nonlinear axisymmetric free vibration analysis of liquid-filled spherical shells with volume constraint condition using membrane theory is presented in this paper. The energy functional of the shell and contained liquid can be expressed based on the principle of virtual work using surface fundamental form and is written in the appropriate forms. Natural frequencies and the corresponding mode shapes for specified axisymmetric vibration amplitude of liquid-filled spherical shells can be calculated by finite element method (FEM). A nonlinear numerical solution can be obtained by the modified direct iteration technique. The results indicate that the Lagrange multiplier is a parameter for adapting the internal pressure in order to sustain the shell in equilibrium state for each mode of vibration with the volume constraint condition. The axisymmetric mode shapes of the liquid-filled spherical shells under volume constraint condition were found to be in close agreement with those in existing literature for an empty spherical shell. Finally, the effects of support condition, thickness, initial internal pressure, bulk modulus of internal liquid, and elastic modulus on the nonlinear axisymmetric free vibration and change of pressure of the liquid-filled spherical shells with volume constraint condition were demonstrated. The parametric studies showed that the change of pressure has a major impact on the fundamental vibration mode when compared with the higher vibration modes.

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Figures

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Fig. 1

Three states of the shell

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Fig. 2

Shell reference surface

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Fig. 3

Typical elements and coordinates

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Fig. 4

Flowchart of the MDIM procedure

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Fig. 5

Convergence of nonlinear axisymmetric frequency of liquid-filled spherical clamped shell

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Fig. 6

Relative amplitude for the first three modes of axisymmetric frequency of liquid-filled spherical clamped shell

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Fig. 7

Axisymmetric mode shapes for liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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Fig. 8

Effects of thickness variation on the first five nonlinear frequency parameters ΩNL=(ρsωn2a2/E′)1/2 of liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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Fig. 9

Effects of thickness variation on the dimensionless internal pressure (λ/p0) in the first five modes of axisymmetric frequency of liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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Fig. 10

Effects of initial internal pressure on the first five nonlinear frequency parameters ΩNL=(ρsωn2a2/E′)1/2 of liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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Fig. 11

Effects of initial internal pressure on the dimensionless internal pressure (λ/p0) in the first five modes of axisymmetric frequency of liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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Fig. 12

Effects of bulk modulus of internal liquid on the first five nonlinear frequency parameters ΩNL=(ρsωn2a2/E′)1/2 of liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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Fig. 13

Effects of bulk modulus of internal liquid on the dimensionless internal pressure (λ/p0) in the first five modes of axisymmetric frequency of liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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Fig. 14

Effects of elastic modulus on the first five nonlinear frequency parameters ΩNL = (ρsωn2a2/E′)1/2 of liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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Fig. 15

Effects of elastic modulus on the dimensionless internal pressure (λ/p0) in the first five modes of axisymmetric frequency of liquid-filled spherical shells: (a) hinged shell and (b) clamped shell

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