Thermoelastic damping in bilayer microbeam resonators with two-dimensional heat conduction

Abstract

Accurate modeling of thermoelastic damping (TED) is a significant and challenging task in the design of multilayer micro-resonator devices. Several analytical models were proposed to predict TED in bilayer and trilayer microbeams. However, previous models theoretically only considered one-dimensional (1-D) heat conduction in the thickness direction. 1-D model cannot capture the effects of length-to-thickness ratio, structural boundary conditions and flexural-mode order, which is only suitable for the long slender beam. To address these issues, this paper presents an analytical TED model based on the two-dimensional (2-D) heat conduction in the thickness and length directions in a bilayer microbeam with a rectangular cross-section. The expression for TED in the form of two infinite series is more explicit and simpler than others. And two key factors that determine the difference between the 2-D model and the 1-D model are first summarized in this paper. The simulation results of the present model match better with those of the finite element method (FEM) than the previous 1-D model. The shape of TED spectrum is affected by the ratio of the thermal diffusivity of materials. Two peaks occur in the case of ratio of thermal diffusivity higher than 100. However, two peaks will reduce to one as the ratio decreases to 1. The convergence rate of the present model is weaker than the 1-D model.