Symplectic wave-based method for the free vibration analysis of cross-ply composite laminated circular cylindrical shells
HAN Shaoyan1，LI Yuyin2，GAO Ruxin3,4
1.Department of Mechanical Engineering, Xi’an Jiaotong University City College, Xi’an 710018, China;
2.Zhuzhou CRRC Times Electric Co., Ltd., Zhuzhou 412001, China;
3.Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China;
4.State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
Abstract：A symplectic wave-based method is proposed for the free vibration analysis of cross-ply laminated cylindrical shells with arbitrary boundary conditions. First, based on Kirchhoff-Love's shell theory, the governing equations of a cross-ply laminated cylindrical shell can be established in the symplectic duality system by selecting an appropriate state vector. Secondly, the characteristic equation for cross-ply composite laminated cylindrical shells is derived so that the symplectic eigenproblem can be formed. Finally, the symplectic eigensolution is substituted into the boundary conditions at both ends of the cylindrical shell, and the algebraic equation of the free vibration problem of the cylindrical shell is obtained and then solved to give the natural frequencies and modals of cross-ply composite laminated cylindrical shells. Numerical examples are given to shown the validity and accuracy of the present method through comparing the results obtained using the present and other methods.
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