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

[+] Author and Article Information
Weeraphan Jiammeepreecha

Department of Civil Engineering, Faculty of Engineering and Architecture, Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand

Somchai Chucheepsakul

Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand

1Corresponding author.

ASME 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 are written in the appropriate forms. Natural frequencies and corresponding mode shapes for specified axisymmetric vibration amplitude of liquid-filled spherical shells can be calculated by finite element method. A nonlinear numerical solution can be obtained by the modi?ed 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 constraint volume 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 constraint volume were demonstrated. The parametrically 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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