Homotopy Perturbation Method for Nonlinear Vibration Analysis of Functionally Graded Plate

In this paper, the Homotopy perturbation method (HPM) is used to analysis the geometrically nonlinear vibrations of thin rectangular laminated functionally graded material (FGM) plates. The Von Karman's strain-displacement relations have been employed to model structural nonlinearity of the system. The material properties of the plate are assumed to be graded continuously in direction of thickness. The effects of initial deflection, aspect ratio and material properties are investigated. Based on the results of this study, the first order approximation of the HPM leads to highly accurate solutions for geometrically nonlinearity vibration of FGM plates. Moreover, HPM in comparison with other traditional analytical methods (e.g., perturbation methods) has excellent accuracy for the whole range of oscillation amplitude and initial conditions.