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.

考虑到导热尺寸（HCD）并采用双相滞后（DPL）非傅立叶理论，首先是矩形截面微/纳米环谐振器的热弹性阻尼（TED）和频移分析模型以本系列的系列形式派生。在建模过程中，重点之一是考虑一维（1D）和二维（2D）导热的耦合热弹性控制方程的估计和求解。试验函数的正交积分方法用于求解温度分布函数。通过能量定义方法和复频方法获得的TED表达式都得到了证明。将先前的模型与当前提出的模型进行比较。研究了双相滞后非傅里叶效应（DPL-NF），HCD，材料选择以及双相滞后时间比对TED的影响。还检查了TED和频移对涉及环的平均半径和径向深度以及模态阶数的几何参数的依赖性。结果表明，HCD和DPL-NF效应显着影响TED频谱和频移。