Large amplitude vibration of initially stressed orthotropic plates

Nonlinear equations of motion are derived for an orthotropic plate in a general state of nonuniform initial stress. The equations include the effects of transverse shear and rotary inertia. The large amplitude free vibrations of a simply supported rectangular orthotropic thick plate subjected to arbitrary initial stresses are also investigated. A combination of pure bending stress plus an extensional stress is taken to be the initial stress in the plane of the plate. 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. The effects of the material properties, initial stress, and vibration amplitude on frequency ratio are studied.