Thermoelastic damping analysis of double clamped microbeams with exponentially tapered thickness

Abstract

For microbeam resonators operated in vacuum, thermoelastic damping (TED) has been theoretically and experimentally verified as a fundamental mechanism of energy loss. Especially, the upper limitation of quality factor of resonators is determined by thermoelastic damping. There are two classical models developed by Zener and Lifshits and Roukes (LR) for evaluating TED. However, the classical models are imprecise to calculate TED values of non-uniform microbeams. In this study, a modified TED model for non-uniform microbeams with exponentially tapered thickness is proposed basing on Zener's theory. The constraint boundary condition of doubly clamped usually encountered in MEMS field is taken into account. The modal parameters of non-uniform beams considered in this work are solved by the modified Adomian decomposition method. Results show that TED values of the present model agree well with those of the finite element method (FEM) model. At low frequencies, TED values of exponentially tapered microbeams are lower than those of uniform microbeams. Additionally, the value of Debye peak of exponentially tapered microbeams is approximately $\pmb{0.474\Delta_{\mathrm{E}}}$ that is lower than $\pmb{0.5\Delta_{\mathrm{E}}}$ of the uniform microbeam.