Nonlinear vibration of initially stressed hybrid composite plates on elastic foundations

Nonlinear vibration equations of motion based on the Mindlin plate theory are derived for a hybrid composite plate with an initial stress on elastic foundations. Using the governing equations derived, the nonlinear vibration behavior of an initially stressed hybrid composite plate on Pasternak and Winkler elastic foundations is studied. The initial stress is taken to be a combination of a pure bending stress and a tensile stress in the plane of the plate. The Galerkin method is employed to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations, and the Runge–Kutta method is used to obtain the nonlinear frequencies. The linear frequency can be calculated by neglecting the nonlinear terms in the ordinary nonlinear differential equations. The results obtained reveal that the foundation stiffness and initial stresses lead to a drastic change in the nonlinear vibration behavior of the plate. The effects of various parameters on the nonlinear vibration of hybrid composite plates are investigated and discussed.