Analysis of free vibration of functionally graded material micro-plates with thermoelastic damping

摘要

This paper presents a theoretical investigation on the response of free vibration of functionally graded material (FGM) micro-plates with thermoelastic damping (TED). Continuous through thickness variation of the mechanical and thermal properties of the FGM plate is considered. By employing the simplified one-way coupled heat conduction equation and Kirchhoff's plate theory, governing equations for the free vibration of the FGM micro-plates with thermoelastic coupling effect are established, in which stretching-bending coupling produced by the material inhomogeneity in the thickness direction is also considered. The heat conduction equation with variable coefficients is solved effectively by a layer-wise homogenization approach. Harmonic responses of the FGM micro-plates with complex frequency are obtained from the mathematical similarity between the eigenvalue problems of the FGM micro-plate with TED and that of the homogenous one without TED. The presented analytical solutions are suitable for evaluating TED in FGM micro-plates with arbitrary through-thickness material gradient, geometry and boundary conditions. Numerical results of TED for a ceramic-metal composite FGM micro-plate with power-law material gradient profile are illustrated to quantitatively show the effects of the material gradient index, the plate thickness, and the boundary conditions on the TED. The results indicate that by adjusting the physical and geometrical parameters of the FGM micro- plate, one can get the minimum of the TED which is even smaller than that of the pure ceramic resonator.