Nonlinear free and forced vibration analysis of thin circular functionally graded plates

In this paper, a semi-analytical approach for nonlinear free and forced axisymmetric vibration of a thin circular functionally graded plate is developed. The plate thickness is constant. Functionally graded material (FGM) properties vary through the thickness of the plate. For harmonic vibrations, by using assumed-time-mode method and Kantorovich time averaging technique, the governing equations are solved. Steady-state free and forced vibration analysis is investigated in detail and corresponding results at uniform ambient temperature are illustrated. Some of these results in special cases are verified by comparing with those in the literature. The results show that the free vibration frequencies are dependent on vibration amplitudes, and that the volume fraction index has a significant influence on the nonlinear response characteristics of the plate.