Application of first-order shear deformation theory for the vibration analysis of functionally graded doubly-curved shells of revolution

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