Vibration of layered shells

The general equations of motion including the effect of shear deformations, for the analysis of symmetrically layered general orthotropic shells and non-symmetric cross-ply shells, are derived. The general procedure in the derivation is similar to that presented by Whitney for such plates, the gross laminate behaviour being taken into consideration, and is based on Ambartsumyan's theory. The general shell equations are reduced to those of a cylindrical shell. The free vibration frequencies are calculated for symmetrically layered specially orthotropic cylindrical shells and non-symmetric cross-ply cylindrical shells. Only freely supported boundary conditions are considered. For comparison, the frequencies are also calculated by Donnell's theory and classical theory. Donnell's theory gives higher value of frequencies than the present theory for cylindrical shells having higher value of thickness to radius ratios as well as having higher value of length to radius ratios. The frequencies given by classical theory lie between those of present theory and Donnell's theory, and their deviation from the present theory depends on the values of axial and circumferential wave numbers, and also on the thickness to radius ratio of the cylindrical shell.