Analytical solution for vibration of generally laminated conical and cylindrical shells

Abstract

In the present study, a simple analytical method is introduced for determination of natural frequencies of generally laminated conical and cylindrical shells with arbitrary boundary conditions. The governing equations of motion employed are those of thin-walled shell theory of Donnell. The free-vibration equations are solved using state space method and series solution in meridional direction. The results are compared and validated with the available especial results in the literature. The effects of bending-stretching coupling, semi-vertex angle, meridional length, shell thickness, fiber directions of composite plies, and lamination sequences on the natural frequency of conical and cylindrical shells are further investigated and presented.