A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton’s principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters on the composite shell, such as length to radius ratios, thickness to radius ratios and elastic restrained constants.

A semi-analytical model is proposed in this study to investigate the in-plane vibration behavior of porous annular plate with porosity distributions in the thickness and radial directions. A variational method combined with a multi-segment technique is employed to establish the theoretical model of elastic restrained porous annular plate. Admissible functions of each plate segment are expanded in the mixed series form, that is, the Jacobian orthogonal polynomial for radial variables and Fourier series for circumferential variables. The boundary penalty parameters are introduced to implement different boundary restrictions and the coupling penalty parameters are employed for ensuring the continuity conditions between segments. A series of numerical examples are given to discuss the convergence characteristics and numerical stability of the current model. The comparison between modal tests and numerical predictions shows that good prediction capabilities with acceptable errors are achieved by the proposed method. The influences of geometrical and material parameters on the in-plane vibration characteristics of porous annular plate are also discussed in detail.