A semi analytical method for free vibration analysis of composite laminated cylindrical and spherical shells with complex boundary conditions

Abstract

A semi analytical method is employed to analyze free vibration behaviors of composite laminated cylindrical and spherical shells subject to complex boundary conditions. The analytical model is established on the basis of multi-segment partitioning strategy and first-order shear deformation theory. The displacement functions are made up of the Jacobi polynomials along axial direction and Fourier series along circumferential direction. In order to obtain continuity conditions and satisfy complex boundary conditions, the penalty method about spring technique is adopted. The solutions about free vibration behaviors of composite laminated cylindrical and spherical shells were obtained by approach of Rayleigh–Ritz. The convergence study and numerical verifications for composite laminated cylindrical and spherical shells with different boundary conditions, Jacobi parameters, spring parameters and truncation of permissible displacement functions are carried out. Through the comparison and analysis study, it is obvious that the proposed method has a good stable and rapid convergence property and the results of this paper closely agreed with those obtained by published literatures, FEM and experiment. In addition, some interesting results about free vibration characteristics of composite laminated cylindrical and spherical shells are investigated.