Nonlinear Vibration of Orthotropic Plates with Initial Stresses on a Two-parameter Elastic Foundation

Nonlinear partial differential equations for vibration of an orthotropic thick plate on a two-parameter (Pasternak type) elastic foundation subjected to a nonuniform initial stress are derived. Both rotary inertia and transverse stress are considered in the derivation. The Galerkin method is used to transform the governing nonlinear partial differential equations to ordinary nonlinear differential equations and the Runge–Kutta method is used to obtain the ratio of nonlinear to linear frequency. Numerical examples are presented for the combination of pure bending stresses and extensional stresses are taken to be the initial stresses in the plane of the plate. These equations are then applied to a simply supported orthotropic plate on a Pasternak foundation to solve its motion of nonlinear vibration. The effects of the material properties, initial stress, amplitude of vibration, and foundation stiffness on frequency ratio are discussed.