Analysis of thermoelastic damping in the clamped-free microbeam with linearly tapered circular cross-section

Abstract

An accurate estimation of thermoelastic damping (TED) is of significance and importance in the design for the microbeam resonators with variable cross-section operated in vacuum. TED determines the up limit of quality factor (Q-factor) used for evaluating the microresonator performance. However, in the past, the previous works focus on the TED modelling of uniform microbeam resonators with rectangular cross-section. There is lack of works aiming at the TED modelling of non-uniform microbeam resonators with circular cross-section. In addition, the previous TED model developed by Zener for uniformly circular cross-section beams is not suitable for calculating TED values of the non-uniform beams. Therefore, the TED model for clamped –free microbeam resonators with linearly tapered circular cross-section is meaningful to be derived in this work. The radius and length dependences of TED are investigated. The results of finite element method (FEM) model are calculated for purpose of comparison. Results indicate that for large aspect ratio (l/r0), TED values of linearly tapered microbeams with circular cross-section are larger than those of uniform microbeams, while for small aspect ratio (l/r0), TED values of linearly tapered microbeams are lower than those of uniform microbeams. Moreover, the maximum values of TED called Debye peaks in linearly tapered microbeams are lower than those of uniform microbeams.