Imperfection sensitivity in the nonlinear vibration oscillations of initially stressed plates

In this paper, nonlinear partial differential equations for the vibrating motion of an initially stressed imperfect isotropic plate are presented. The derived equations include the effects for imperfections, transverse shear deformation, rotary inertia and non-uniform initial stresses. Using these derived governing equations, the nonlinear vibration of initially stressed plates with initial imperfection is studied. Present approach employs perturbation technique, Galerkin method and Runge-Kutta method. The perturbation technique was used to derive the nonlinear governing equations. The motion of imperfect plates is obtained by performing the Galerkin method and then solved by Runge-Kutta method. Numerical solutions are presented that relate to the performances of perfect and imperfect plates. A combination of pure bending stress plus an extensional stress is taken to be the initial stress in the plane of the plate. It is found that the existence of initial stresses and geometric imperfection may result in a drastic change on the nonlinear vibration behavior. The effects of various parameters on the nonlinear free vibrations of imperfect plates are presented.