Modelling and evaluation of thermoelastic damping of FGM micro plates based on the Levinson plate theory

摘要

Thermoelastic damping (TED) in a simply supported functionally graded material (FGM) micro rectangular plate is investigated analytically based on the higher-order shear deformation plate theory. The equations of motion for the thermo-elastic coupled transverse free vibration and the heat conduction equation coupled are derived based on the Levinson plate theory and the one-way coupled heat conduction theory. A semi-analytical solution of the heat conduction equation with variable coefficients is obtained by using a layer-wise homogenization approach. The complex frequency of the micro plate including TED is determined in terms of the frequency of the corresponding isothermal homogenous Kirchhoff plate by using the mathematical similarity between the eigenvalue problems for the two types of plates. The effects of the shear deformation, the material gradient and the geometry on the TED are examined in detail for the FGM micro plate made of ceramic-metal constituents with the power-law gradient profile. The numerical results show that the TED evaluated by the Levinson plate theory is smaller than that by the Kirchhoff plate theory. Therefore, for a thick or moderately thick micro plate the Levinson plate theory can provide a more accurate prediction of the TED than the Kirchhoff plate theory.