Forced vibration analysis of thin cross-ply laminated circular cylindrical shells with arbitrary boundary conditions using the symplectic wave-based method

Abstract

A symplectic wave-based method is proposed in this paper for the forced vibration analysis of thin cross-ply laminated cylindrical shells with arbitrary boundary conditions. Firstly, based on Kirchhoff–Love’s shell theory, the unified governing equation of thin cross-ply laminated cylindrical shells in the symplectic duality system is established by selecting an appropriate state vector, which leads to the transformation of the vibration analysis of cylindrical shells from two-dimensional to one-dimensional. Then, the response of laminated cylindrical shells can be described in terms of wave shapes in the symplectic duality system. The relationship between incident and reflected waves at a boundary is established to analytically describe the boundary condition, which allows the present method to deal with arbitrary boundary conditions and has high computational accuracy. Finally, the displacement and internal force responses can be simultaneously and explicitly calculated by using the adjoint symplectic orthogonal relation of wave shapes in the symplectic duality system, which ensures that the present method has high computational efficiency. The present method has truncation errors only in the circumferential direction, and is analytical in the axial direction, which can lead to a high accuracy and convergence rate. Several examples demonstrate the effectiveness, convergence and accuracy of the present method, as well as its ability to handle arbitrary boundary conditions.