Nonlinear vibration of laminated plates on a nonlinear elastic foundation

Nonlinear partial differential equations of an initially stressed laminated plate resting on a nonlinear Winkler elastic foundation are derived in this paper. The equations include the effects of transverse shear and rotary inertia. The Galerkin’s approximate method is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations and the Runge–Kutta method is used to obtain the ratio of nonlinear frequency to linear frequency. The initial stress is a combination of a pure bending stress and an extensional stress in the plane of the plate. The effects of various parameters on the nonlinear vibrations are presented. It is found that the frequency responses of nonlinear vibration are sensitive to the vibration amplitude, modulus ratio, foundation stiffness and initial stresses.