Thermoelastic damping in the out-of-plane vibration of a microring resonator with rectangular cross-section

Abstract

An analytical model is proposed for thermoelastic damping in the out-of-plane vibration of a microring resonator with rectangular cross-section. Although thermoelastic damping in the in-plane vibration of a ring resonator has been intensively studied, there have been few works on thermoelastic damping of microring resonators in out-of-plane mode. The main difficulty of estimating thermoelastic damping could be the coupled motion of bending and torsion in out-of-plane mode. This paper considers the coupled motion and derives a closed-form expression of thermoelastic damping in a microring resonator under out-of-plane vibration. The temperature field, caused by the bending component, is obtained by considering only the heat flow in axial direction of the ring section. The theory calculates the energy loss caused by thermoelastic damping associated with pure bending component and the energy stored caused by both bending and torsion components. Furthermore, a reduced model of thermoelastic damping is proposed for the ring of square cross-section. The present model is validated by the comparison with the finite-element method (FEM). The relationships between structural dimensions, driving force and thermoelastic damping are investigated. It is found that the results of the present model show a good agreement with the numerical results, especially for the case of square cross-section.