Thermoelastic Damping in Micro- and Nanobeam Resonators With Non-Fourier Heat Conduction

Abstract

Predicting thermoelastic damping (TED) under the effect of non-Fourier heat conduction is challenging and crucial for the design of micro- and nanobeam resonators with high quality factors. In the past, many works were devoted to the modeling of TED under the effect of non-Fourier heat conduction. Some analytical and numerical results for TED were presented. However, the spectrum of TED contains multiple peaks only in the numerical results. The previous analytical model failed to give a reasonable prediction for the multiple-peak phenomenon. Few works can give a convincing explanation for the existence of multiple peaks. In this paper, the TED in micro- and nanobeam resonators under the effect of non-Fourier heat conduction is investigated using the generalized thermoelasticity theory with single-phase-lag time. An analytical formula of TED is obtained in the form of infinite series. The effects of non-Fourier heat conduction on TED are studied for representative cases of the micro- and nanobeams. A simple analytical expression for the accurate determination of the multiple peaks in TED is obtained. The results of the present model agree well with the numerical results available in the reported literature. The results of this paper may bring new insights for the multiple-peak phenomenon of TED spectrum in micro- and nanobeams.