Accurately estimating thermoelastic damping (TED) is of significance for the design of micro/nano-resonators with high quality factor. This work aims at providing new investigation of TED with considering the non-Fourier heat conduction (NFHC) effect and the size-dependent effects in the thermal and mechanical fields. Analytical models of TED in rectangular and circular micro/nanoplate resonators are firstly developed in the theoretical frameworks of nonlocal dual-phase-lagging (DPL) model and the modified couple stress (MCS) model. The governing equation of coupled thermoelasticity is modeled by adopting the nonlocal DPL theory, and the solution of dilatation temperature is solved by utilizing the trial-function method. The energy-definition approach is used to obtain TED expressions, in which the maximum stored energy includes the classical elastic potential energy and the MCS potential energy. Two representative materials involving the semiconductor silicon and the metal gold with typical thermal and mechanical length parameters and DPL times are selected in simulation. The influences of material intrinsic parameters on TED spectra, which include the DPL times, the MCS length parameter, and the nonlocal thermal length parameter referring to the mean free path, are investigated. TED spectra obtained by the classical models are also plotted for comparison. The results indicate that TED in micro/nanoplate resonators depends significantly on the DPL-NFHC effect and the nonlocal thermal size-dependent effect. Moreover, TED can be reduced by the MCS size-dependent effect resulting in improving the quality factor.

准确估算热弹性阻尼（TED）对于设计高品质因数的微/纳米谐振器至关重要。这项工作旨在通过考虑非傅里叶热传导（NFHC）效应以及热和机械领域中与尺寸有关的效应来提供对TED的新研究。首先在非局部双相滞后（DPL）模型和修正耦合应力（MCS）模型的理论框架下，开发了矩形和圆形微/纳米板谐振器中的TED分析模型。采用非局部DPL理论对耦合热弹性控制方程进行建模，并采用试函数法求解膨胀温度问题。能量定义方法用于获得TED表达式，其中最大存储能量包括经典弹性势能和MCS势能。在仿真中选择了两种具有代表性的材料，包括半导体硅和金属金，这些材料具有典型的热和机械长度参数以及DPL时间。研究了材料固有参数对TED光谱的影响，包括DPL时间，MCS长度参数和参考平均自由程的非局部热长度参数。还绘制了通过经典模型获得的TED光谱以进行比较。结果表明，微/纳米板谐振器中的TED很大程度上取决于DPL-NFHC效应和非局部热尺寸依赖性效应。此外，可通过MCS尺寸依赖性效应降低TED，从而提高品质因数。