Thermoelastic damping in micro-disk resonators with in-plane extensile vibration

Thermoelastic damping (TED), as a fundamental energy dissipation mechanism, establishes the theoretical upper bound for the quality factor (Q) in micro-resonators. In this study, an explicit TED model is developed for the micro-disk resonators with in-plane extensile vibration for the first time. The proposed TED model, formulated in a series form, demonstrates remarkable performance of convergence. The theoretical Q values predicted by the present developed TED model show excellent agreement with the finite-element results. The distributions of fluctuating temperature, which are assumed to be the summation of thermal modes, are influenced by both the vibration frequency and thermal relaxation time. Notably, an oscillating phenomenon of the imaginary part of fluctuating temperature will appear when the radius of the micro-disk is sufficiently large. The findings indicate that the primary TED components associated with nearly the first ten thermal modes can predominantly govern the overall characteristics of a TED spectrum. Furthermore, from a design perspective, optimal performance of high-Q micro-disk resonators with in-plane extensional vibration can be achieved by selecting the fundamental vibration mode and utilizing silicon as the structural material, due to its superior thermomechanical properties.