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

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 QTED of the contour-mode vibrations of a circular thin-plate resonator is well above 1×106 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.