Non-linear vibration of initially stressed hybrid composite plates

Non-linear partial differential equations based on the Reissner–Mindlin plate theory are derived for large amplitude vibration of a hybrid composite plate in a general state of non-uniform initial stress. The equations include the effects of transverse shear and rotary inertia. Using these derived governing equations, the large amplitude vibration of an initially stressed hybrid composite plate is studied. The initial stress is taken to be a combination of pure bending stress and a uniform normal stress in the plane of the plate. The Galerkin method is used to reduce the governing non-linear partial differential equations to ordinary non-linear differential equations and the Runge–Kutta method is used to obtain the non-linear frequencies. The linear frequency can be obtained by neglecting the non-linear terms in ordinary non-linear differential equations. The non-linear vibration frequencies are sensitive to the vibration amplitude, elastic modulus, laminate stacking sequence and state of initial stresses. The effects of various parameters on the large amplitude free vibrations are presented.