Analytical solution of thermoelastic damping in Levinson microrectangular plate resonators

Based on Levinson's higher-order shear deformation plate theory，accurate analytical solutions for the complex natural frequency and the field of temperature change of a simply supported rectangular micro plate resonator in thermoelastic coupled free vibration are obtained. Furthermore，inverse quality factor representing the TED is extracted by using the complex frequency approach. Numerical results are presented to show the variation regulation of the TED versus the aspect ratio of the micro Levinson plate in different vibration modes. By comparing the values of TED based on the Levinson plate theory with those based on both Mindlin and Kirchhoff plate theories，the level of effect of shearing deformation on the TED is analyzed. The numerical results show that for the moderate thick and thick plate resonators the values of TED evaluated by the classical plate theory are obviously greater than that by shearing strained plate theory. It is because that the classical plate theory ignores the transvers shear deformation and over estimates the rigidity of the structure. In addition，the comparison between the predicted values of TED of Mindlin and Levinson microplates with four simply supported edges is given. As a result，Levinson higher-order shear deformation plate theory can better predict the TED of the thick microplate，because the displacement field of Levinson plate theory can accurately satisfy the stress-free conditions at the upper and lower surface and the temperature field contains the higher order term of the through-thickness coordinate.