A Numerical Model for Thermoelastic Damping in Micromechanical Resonators Made From Anisotropic Materials

This paper presents a numerical model for thermoelastic damping (TED) in micromechanical resonators made from anisotropic materials, such as single crystal silicon. It is built upon a thermal-energy method, in which TED is interpreted as the generation of thermal energy per cycle of vibration and consequently the mathematical expression for TED is derived from the linear thermoelastic governing equations for anisotropic media. This numerical model consists of two sequential numerical simulations: elastic vibrations and transient heat conduction, and is developed in the ANSYS/Multiphysics, giving rise to the numerical value for the derived expression for TED and further the quality factor related to TED (Q_TED) in a micromechanical resonator with any complex structural geometry. Through comparison with experimental data in the literature, the validity of the presented numerical model is demonstrated.