Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates

In this paper, the nonlinear free axisymmetric vibration of a thin circular functionally graded plate in thermal environment is formulated in terms of von-Karmanʹs dynamic equations, and a semi-analytical approach is developed. The plate thickness is constant and the material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. For harmonic vibrations, by using assumed-time-mode method and Kantorovich time averaging technique, governing equations are solved. The nonlinear frequencies and associated stresses are determined at large amplitudes of vibration. Effects of material compositions and thermal loads on the vibration characteristics and stresses are examined. The numerical results obtained here are compared with available published results, based on various approaches.