Dual-phase-lagging thermoelastic damping and frequency shift of micro/nano-ring resonators with rectangular cross-section

摘要

Considering the heat-conduction dimension (HCD) and adopting the dual-phase-lagging (DPL) non-Fourier theory, analytical models of thermoelastic damping (TED) and frequency shift for the rectangular cross-section micro/nano-ring resonators are first derived in the series form in this work. In the modeling procedure, one of emphases is the estimation and solution of the governing equation of coupled thermoelasticity considering one-dimensional (1D) and two-dimensional (2D) heat conduction. The orthogonality-integration method of the trial function is used to solve the temperature profile functions. The TED expressions obtained by the energy-definition approach and the complex-frequency approach are both demonstrated. The previous models are compared with the present proposed models. The influences of the dual-phase-lagging non-Fourier (DPL-NF) effect, HCD, the material selection, and the ratio of dual-phase-lagging times on TED are investigated. The dependences of TED and the frequency shift on the geometrical parameters involving the mean radius and radial depth of the ring, and the modal order are also examined. The results show that TED spectra and frequency shift are significantly affected by the HCD and the DPL-NF effect.