Elastothermodynamic damping modeling of three-layer Kirchhoff–Love microplate considering three-dimensional heat conduction

Elastothermodynamic damping is one of the most important energy loss mechanisms in micro/nano mechanical resonators, which is related to the high sensitivity and high resonance frequency characteristics of resonators. With the wide application of resonators, multilayer microplate resonators have been applied. In this paper, the elastothermodynamic damping models of three-layer of Kirchhoff–Love microplate under three typical boundary support conditions of Clamped-Clamped-Clamped-Clamped (C-C-C-C), Clamped-Free-Clamped-Free (C-F-C-F) and Clamped-Free-Free-Free (C-F-F-F) are established. Firstly, the thermoelastic mechanical equations of the microplate are given, and then the three-dimensional temperature distribution functions of the microplate are obtained based on the generalized orthogonal function method. Finally, the elastothermodynamic damping models are established based on the composite multilayer plate theory. The model in this paper is compared with the previous model and the finite element results.