Nonlinear Free Vibration of Laminated Composite Plates

Abstract

In this paper the nonlinear vibration of composite plates has been presented. Usually in the nonlinear analysis of plates, the von Karman‐type formulation is followed because it is possible to obtain the complete solution once the solution for lateral displacement is assumed. In this paper an extension of the von Karman formulation has been presented for the first time. In this formulation the resulting governing equations are nonlinear in all the displacement parameters of the plate. Due to the highly nonlinear nature of the equations, the straightforward solution techniques usually adopted in the nonlinear plate analysis cannot be used. To circumvent this problem, a regular perturbation technique has been used to obtain the solution. Numerical results presented for simply supported plates indicate that the von Karman‐type formulation is quite satisfactory. This may also be viewed as a validation of the von Karman approach to nonlinear plate analysis.