Nonlinear vibration of initially stressed functionally graded plates

In this paper, nonlinear partial differential equations for the vibration motion of an initially stressed functionally graded plate (FGP) are derived. The formulations are based on the classical plate theory and derived for the nonlinear vibration motion of an FGP in a general state of arbitrary initial stresses. The material properties of the FGP are assumed to vary continuously from one surface to another, according to a simple power law distribution in terms of the constituent volume fractions. The motion of functionally graded ceramic/metal plate is obtained by employing the Galerkin method and then solved by Runge–Kutta method. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the plane of the ceramic/metal plate. It is found that the frequency responses of nonlinear vibration are sensitive of the state of initial stress, the amplitude of vibration and the volume fraction of FGP.