Analytical solution of squeeze film and thermoelastic damping in bulk resonators

Abstract

Bulk micro-resonators exhibit potential applications for timing and frequency control based on their high-quality factor and high frequency. However, performance of bulk resonators is difficult to predict due to the multi-physics nature of system including electrical actuation and vibration behavior. An analytical model of in-plane vibration of bulk resonators that consider effects of squeeze film damping (SFD) and thermoelastic damping (TED) is presented by a modified Fourier series method. The squeeze gas pressure, which generates the equivalent elastic and damping coefficients of gas, is determined by the Reynolds equation using a Green’s function method. The anchor, which links the fixed position and resonator, and the linear electrostatic force are simplified as equivalent but separate springs. Vibration displacement and temperature distributions are calculated by Fourier series coefficients. Numerical results of the effects of SFD and TED on the resonator are solved with a parametric analysis and verified by published data and simulation values of COMSOL®. The coupling effect of SFD and TED and their relative contribution on the bulk resonator are also evaluated. The presented model can guide to explore characteristics of bulk resonators in the presence of SFD and TED.