Nonlinear flexural vibrations of initially deflected cross-ply laminated plates with elastically restrained edges

Based on dynamic Marguerre equations for initially deflected rectangular plates, a series solution is given for large amplitude, free, flexural vibration of a cross-ply laminated plate with elastically restrained edges. By virtue of orthogonal functions the governing equations are reduced to two nonlinear second-order differential equations. Convergent solutions can be determined to any desired degree of accuracy. Using Galerkin procedure and perturbation technique the effects of initial deflections on the nonlinear frequency of the plate is studied.