Free vibration analysis of moderately thick elliptical shells using the dynamic stiffness method
CHEN Xu-dong 1，YE Kang-sheng 2
1. School of Naval Architecture and Civil Engineering, Jiangsu University of Science and Technology, Zhangjiagang 215600,China；
2. Department of Civil Engineering, Tsinghua University; Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Beijing 100084 China
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.
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