Free vibration analysis of uniform and stepped functionally graded circular cylindrical shells

A semi analytical method is employed to analyze free vibration characteristics of uniform and stepped functionally graded circular cylindrical shells under complex boundary conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy complex boundary conditions, the penalty method about spring technique is adopted. The solutions about free vibration behavior of functionally graded circular cylindrical shells were obtained by approach of Rayleigh-Ritz. To confirm the dependability and validity of present approach, numerical verifications and convergence studies are conducted on functionally graded cylindrical shells under various influencing factors such as boundaries, spring parameters <i>et al</i>. The present method apparently has rapid convergence ability and excellent stability, and the results of the paper are closely agreed with those obtained by FEM and published literatures.