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Abstract In this paper, the nonlinear natural vibration of the functionally graded rotating circular plate composed of metal and ceramic in the thermal environment was analyzed, considering the geometric nonlinearity, the effect of temperature on physical properties of the material, and the continuous variations of material properties in the thickness direction that follow a simple power-law distribution in terms of volume fractions of the constituents of the plate. The nonlinear natural vibration equations of the functionally graded rotating circular plate in a high-temperature environment were derived by using Hamilton’s principle. As for the surrounding clamped boundary conditions, the nonlinear differential equation of transverse natural vibration of the circular plate was obtained through the Galerkin method. Moreover, the static deflection induced by the rotation and functional gradient characteristics was determined. Based on the assumption of strong nonlinearity, an improved method of multiple scales was employed to solve the differential equation of natural vibration, and the nonlinear expression for natural frequency was achieved. Through numerical calculations, the changes of natural frequency of the circular plate with rotational speed, temperature, volume fraction, and plate thickness were discussed, respectively. Furthermore, the degenerated model of the system was introduced to verify the rationality of the dynamic model, where the corresponding numerical solutions obtained by the Runge-Kutta method and the periodic graph method were compared with the analytical ones, and the results were basically consistent. It is found that the nonlinear natural frequency increases with the increase of rotating speed or disk thickness, but decreases with the increase of metal content or temperature of the circular plate surface. Especially, when the surface temperatures of both the metal and the ceramic increase at the same time, the nonlinear natural frequency decreases faster. The given natural frequency and mode shape solutions are of practical importance for various engineering dynamic analyses of functionally graded circular plates.
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Received: 02 August 2019
Published: 12 June 2020
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2020, Vol. 41 
