Thermoelastic damping in circular cross-section micro/nanobeam resonators with single-phase-lag time

Abstract

Estimating thermoelastic damping (TED) is a crucial and significant procedure for the design of the high quality-factor micro/nanobeam resonators operated in vacuum. However, most of the previous TED models were derived by employing the classical thermoelasticity theory established on the Fourier heat conduction. These existing models all focused on beam resonators with rectangular cross-section. In this work, employing the generalized thermoelasticity theory of single-phase-lag model, an analytical TED model is derived for circular cross-section micro/nanobeams considering the non-Fourier heat conduction. The influences of non-Fourier effect on TED behaviors and the temperature field of the circular cross-section beam are examined. The single- and multiple-peak phenomena of TED spectrum under the non-Fourier effect are studied. The results indicate that TED in circular cross-section beams is significantly dependent on the equilibrium temperature and the ratio of single-phase-lag time to thermal relaxation time. In addition, the temperature distribution in the beam exhibits distinct differences due to the non-Fourier effect.