An analytical solution for thermoelastic damping in a micro-beam based on generalized theory of thermoelasticity and modified couple stress theory

This paper is aiming to present an analytical method to study on thermoelastic damping (TED) and dynamic behavior of micro-beam resonators as a micro-electro-mechanical system (MEMS) using modified coupled stress theory. Coupled thermoelasticity governing equations of MEMS are derived based on the generalized theory of coupled thermoelasticity with one relaxation time and then is analytically solved by using the Laplace transform techniques for spatial variables. The advantage of presented analytical method is its great capability to solve thermoelastic problems in MEMS under various boundary conditions. The time histories of displacement, deflection and thermal moment in a micro-beam subjected to uniform load and different boundary conditions are obtained and the thermoelastic damping is discussed in details. All unknown parameters are presented in closed forms at Laplace domain. Also, a modified Laplace inverse transform method is employed to obtain the results in time domain. The obtained results based on the presented analytical method show a reasonable agreement with previous published data based on numerical methods.