A thermal-energy method for calculating thermoelastic damping in micromechanical resonators

In this paper, a thermal-energy method is presented for calculating thermoelastic damping in micromechanical resonators. In this method, thermoelastic damping is interpreted as the generation of thermal energy per cycle of vibration and consequently is expressed in terms of entropy—a thermodynamic parameter measuring the irreversibility in heat conduction. As compared with a commonly used complex-frequency method, this thermal-energy method does not involve complex values and thus can be implemented in ANSYS/Multiphysics, a finite element modeling software, with fast speed. Based on the governing equations of linear thermoelasticity, the mathematical expressions are first derived for thermoelastic damping in micromechanical resonators made from isotropic and anisotropic materials, respectively. Through two sequential numerical simulations: uncoupled elastic modal simulation and transient heat conduction, the numerical values for these expressions are then calculated in ANSYS/Multiphysics for micromechanical resonators taking different structural geometries. This method is verified using the well-known theoretical solution to thermoelastic damping in a beam resonator and experimental data. As a result, the developed thermal-energy method can calculate thermoelastic damping in micromechanical resonators with any complex structural geometry and made from isotropic and/or anisotropic materials.