Two-Dimensional Models of Thermoelastic Damping for Out-of-Plane Vibration of Microrings With Circular Cross-Section

Thermoelastic damping is an important dissipation mechanism in microresonators. This article presents an analytical model of thermoelastic damping for out-of-plane vibration of microrings with circular cross-section by considering two-dimensional heat conduction. The temperature field of the circular cross-section is calculated by using the Bessel function and free boundary conditions. The coupled motion of bending and torsion in out-of-plane mode has been considered to calculate the mechanical energy. The derivation shows that the analytical expression of thermoelastic damping can be considered as a product of Zener model and the energy ratio of pure bending energy stored to total elastic energy stored. The present model is verified by comparing with the finite-element method. The convergence of the analytical expression has been examined and the characteristics of the expression have been studied by using a normalized form. The effect of geometry on thermoelastic damping has been studied. The results show that thermoelastic damping in microrings of circular cross-section under out-of-plane mode depends on geometry, scales, and vibration frequencies.