Thermoelastic damping in the contour-mode vibrations of micro- and nano-electromechanical circular thin-plate resonators

Abstract

This paper presents an analytical study on thermoelastic damping (TED) in the contour-mode vibrations of micro- and nano-electromechanical circular thin-plate resonators. Instead of expressing TED in terms of a commonly used complex frequency value, this work calculates TED by using a thermal-energy approach in which the generation of thermal energy per cycle of vibration is considered. To demonstrate its validity, this thermal-energy approach is first utilized to tackle the well-known TED in a flexural-mode beam resonator. Then, it is extended to analyzing TED in the contour-mode vibrations of a circular thin-plate micro-/nano-resonator. Consequently, the behavior of TED versus the key design parameters, namely thin-plate radius and resonant frequency, is predicted, and the attainable quality factors of such type of resonators are defined. From this work, it is found that the Q TED of the contour-mode vibrations of a circular thin-plate resonator is well above 1×10 6 when its resonant frequency is below 1 GHz and TED becomes a significant source of dissipation for circular thin-plate resonators at the nanometer scale.