Thermoelastic damping in functionally graded material circular micro plates

Abstract

In this article, thermoelastic damping (TED) in functionally graded material (FGM) circular micro plates is analyzed based on classical plate theory and one-way coupled heat conduction equation. The material properties are assumed to be varied continuously in the thickness direction of the plate. A one-way coupled heat conduction equation with variable coefficients is solved by using a layer-wise homogenization approach. The complex frequency, including TED, of the FGM micro plate is obtained in terms of the natural frequency of the corresponding isothermal homogenous plate without TED from the mathematical similarity between the eigenvalue problems of governing differential equations of the two kind structures. Numerical results of TED for a ceramic-metal composite FGM circular micro plate are presented quantitatively to show the effects of the material gradient index, the geometry, the vibration mode shapes, and the environmental temperature on the TED in detail. The present mathematical model and solution method can be also used to evaluate TED in the FGM circular and annular plates with other through-thickness material gradient forms.