Single-phase-lag thermoelastic damping models for rectangular cross-sectional micro- and nano-ring resonators

Abstract

Employing the non-Fourier theory of single-phase-lag (SPL) model, the analytical thermoelastic damping (TED) models for rectangular cross-sectional micro- and nano-ring resonators with heat conduction along the radial thickness direction and the circumferential direction are derived in this paper. Specially, for only considering one-dimensional (1D) heat conduction along the radial thickness direction, the 1D-SPL TED model of the ring derived is consistent with that of the beam reported previously. The dependence of TED behaviors on the single-phase-lag time, geometry dimensions, the modal order, the material type, and the equilibrium temperature is explored. The TED spectra with single- or multiple-peak phenomenon under the effect of single-phase-lag time are discussed, which can be completely characterized by the present models in the series form. The results reveal that the dimensions of heat conduction and the effect of single-phase-lag time have significant influences on TED behaviors of micro- and nano-ring resonators.