On free vibration of cross-ply laminates in cylindrical bending

Abstract

Cylindrical bending problem is one of the simplest problems of laminated plates [1]. Pagano [2] first derived an exact static three-dimensional (3-D) solution of cross-ply laminates subject to cylindrical bending. He further presented an exact solution of angle-ply laminates [3]. Pagano’s two exact solutions are only restricted to a laminate where edges are simply supported. Studies on other type boundary conditions basically based on various plate theories are carried out, and significant achievements have been made recently [4–6]. Differential quadrature method (DQM) has been proved to be very effective in solving differential equations governing beam/plate/shell deformations and vibrations [7–9]. On the other hand, the state-space method (SSM) is very effective in analyzing laminated structures [10–13]. However, exact solutions are available only for simply supported conditions. To overcome this difficulty, Chen et al. [14] recently developed a semi-analytical method combining DQM and SSM together and successfully analyzed the free vibration of sandwich beams. The method allows us to deal with different boundary conditions exactly that the Saint-Venant principle becomes unnecessary in the analysis. In this paper, the method is extended to analyze the free vibration of cross-ply laminates in cylindrical bending. The results presented here are believed to be valuable, especially those for thick laminates with non-simply supported conditions.