Evaluation of thermoelastic damping in micromechanical resonators with axial pretension: An analytical model accounting for two-dimensional thermal conduction

It has been reported that application of tensile axial stress can simultaneously increase quality factor and resonant frequency for micromechanical resonators. In this study, we formulate an analytical model for evaluating thermoelastic damping in micromechanical resonators based on the thermal energy method, in which thermal conductions in both thickness direction and axial direction are considered. An explicit expression for thermoelastic damping in the form of infinite series has been obtained. The proposed analytical model is further validated by finite element analysis. Results of the present study demonstrate that the 2D model needs to be adopted in order to accurately evaluate thermoelastic damping of micromechanical resonators with axial pretension. In addition, the 2D model proposed in the present study eliminates the inherent inconsistency entailed in the 1D model.