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Li Shirong. Thermoelastic damping in functionally graded Mindlin rectangular micro plates. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1601-1612. DOI: 10.6052/0459-1879-22-055
 Citation: Li Shirong. Thermoelastic damping in functionally graded Mindlin rectangular micro plates. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1601-1612. DOI: 10.6052/0459-1879-22-055

# THERMOELASTIC DAMPING IN FUNCTIONALLY GRADED MINDLIN RECTANGULAR MICRO PLATES

• Accurately modelling and evaluating of thernoelastic damping (TED) in functionally graded material (FGM) micro plates are challenging novel topics in the study on the responses of thermoelastic coupled vibration of this kind of new type micro resonators. In this paper, TED in a simply supported FGM rectangular micro plate with moderate thickness is investigated by means of mathematical analysis. Based on the Mindlin plate theory and the one-way coupled heat conduction theory, differential equations governing the thermal-elastic free vibration of the FGM micro plates with the material properties varying continuously along with the thickness direction are established. Under the adiabatic boundary conditions at the top and the bottom surfaces, analytical solution of the temperature field expressed by the kinematic parameters is obtained by using layer-wise homogenization approach. As a result, the structural vibration equation including the thermal membrane force and moment is transformed into a partial differential equation only in terms of the amplitude of the deflection. Then, by using the mathematical similarity between the eigenvalue problems an analytical solution of the complex frequency for an FGM Mindlin micro plate with the four edges simply supported is arrived at, from which the inverse quality factor representing the TED is extracted. Finally, numerical results of TED for the FGM rectangular micro plate made of ceramic-metal constituents with the material properties varying in the thickness as power functions are presented. Effects of the transverse shear deformation, the gradient of the material property and the geometric parameters on the TED are quantitatively investigated in detail. The numerical results show that the TED evaluated by the Mindlin plate theory is smaller than that by the Kirchhoff plate theory and that the difference in the values predicted by the two plate theories becomes significant along with the increase of the thickness-to-side length ratio.

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