Nonlocal dual-phase-lag thermoelastic dissipation of size-dependent micro/nano-ring resonators

Abstract

The modeling of thermoelastic damping or dissipation (TED) is significant but challenging for the quality-factor estimation of the size-dependent micro/nano-resonator operating in some extreme situations, such as the ultra-instantaneous thermal heating and ultra-high frequency excitation. Considering these special situations, this study intends to explore the more generalized TED mechanism for the micro/nano-ring resonator with the size-dependent effect and non-Fourier heat conduction effect. In this work, one/two-dimensional (1D/2D) TED models of rings are firstly developed by adopting the nonlocal dual-phase-lag (DPL) model and the modified-couple-stress (MCS) model. In detail, the size-dependent effects both in the elastic and thermal fields are respectively characterized by the length-scale parameters lQ and lM, while the effect of non-Fourier heat conduction is characterized by DPL times τQ and τT. In simulations, two typical materials involving silicon and gold popularly manufactured in micro/nano-devices are selected, and the results obtained by previous models are shown for comparison. Firstly, the fluctuation temperature and TED spectra under the MCS size-dependent and nonlocal-DPL effects are investigated. Secondly, the peak phenomenon of TED spectra is analyzed, then the equivalent relaxation times for the 1D case are discussed according to the peak-frequency calculation. Results demonstrate that the MCS size-dependent effect can slightly improve the quality factor of the ring by weakening TED, but its existence should be recognized. Meanwhile, thermal behaviors of solid resonators at micro/nano-scales are jointly affected by the amount relationship of τ1, τQ, τT, and τl. When the characteristic dimension of the resonator is in the level of lQ referring to the mean-free path of energy carries, the nonlocal size-dependent effect is necessary to be considered.