Large-amplitude vibration of an initially stressed thick circular plate

In this paper, nonlinear equations of motion are derived for a transversely isotropic thick circular plate in a general state of nonuniform initial stress. The equations include the effects of transverse shear and rotary inertia. The large-amplitude flexural vibrations of simply supported and clamped thick circular plates subjected to initial stress are also investigated. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the plane of the plate. Nonlinear equations of motion are used to solve the vibration problems by the Galerkin method. In addition, the effects of various parameters on the nonlinear vibration frequencies are studied.