STRONGLY NONLINEAR RESONANCE ANALYSIS OF FUNCTIONALLY GRADED MATERIAL RECTANGULAR PLATES

A ceramic/metal functionally graded rectangular plate is considered in this study. Based on the stress-strain relationship and nonlinear geometric equations, the nonlinear partial differential equations of a FGM plate subjected to a transverse harmonic excitation are derived by using the principle of virtual work. For the simply supported rectangular plate, the Duffing strongly nonlinear vibration equation is obtained by using Galerkin method. Using the modified multi-scale method, the strongly nonlinear primary resonance is solved and the amplitude-frequency response equation is obtained. The stationary frequency-response curves and phase trajectory of the functionally graded plate are plotted. The effects of different parameters are discussed. Also, the results by modified multi-scale method are contrasted with those by a classical multi-scale method.