Free vibration analysis of moderately thick elliptical shells&nbsp;using the dynamic stiffness method

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (6) : 85-90.

Free vibration analysis of moderately thick elliptical shells using the dynamic stiffness method

CHEN Xu-dong 1，YE Kang-sheng 2

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Abstract

The application of exact dynamic stiffness method to the free vibration analysis of moderately thick elliptical shells is introduced. The free vibration of moderately thick elliptical shells is decomposed into a series of one-dimensional vibration problems with respect to different circumferential wave numbers. For any one-dimensional vibration problem, governing equations are written in Hamiltonian form from which the dynamic stiffness relationship of this one-dimensional problem is set up. Based on this dynamic stiffness relationship, the governing equations are solved by using the ordinary differential equations (ODE) solver COLSYS from which element dynamic stiffnesses can be obtained. By applying the Wittrick-Williams algorithm, natural frequencies under a specific circumferential wave number are found. Numerical examples on moderately thick spherical and elliptical shells with different boundary conditions are given, showing that the dynamic stiffness method is robust, reliable and accurate.

Key words

elliptical shells / free vibration / dynamic stiffness method / Wittrick-Williams algorithm / Hamiltonian form

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CHEN Xu-dong 1，YE Kang-sheng 2. Free vibration analysis of moderately thick elliptical shells using the dynamic stiffness method[J]. Journal of Vibration and Shock, 2016, 35(6): 85-90

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