Abstract This paper deals with the small-scale effects on the thermoelastic damping (TED) in microplates. The coupled equations of motion and heat conduction are provided utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model. Solving these equations and adopting the Galerkin method, the real and imaginary parts of frequency are extracted. The complex frequency approach is then employed to present a size-dependent expression for evaluating TED in thin plates. An analytical expression for TED incorporating small-scale effects is also derived on the basis of the energy dissipation approach. To survey the effect of different continuum theories on TED, the results obtained by SGT are compared with those predicted by the modified couple stress theory (MCST) and the classical continuum theory. Furthermore, through a number of parametric studies, the effects of some variables on the amount of TED, such as microplate thickness, type of material and boundary conditions are discussed.

中文翻译：

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根据广义热弹性理论在应变梯度微板中的热弹性阻尼

摘要 本文研究了微孔板中热弹性阻尼 (TED) 的小尺度效应。利用应变梯度理论 (SGT) 和双相滞后 (DPL) 热传导模型提供了运动和热传导的耦合方程。求解这些方程并采用伽辽金方法，提取频率的实部和虚部。然后采用复频率方法来呈现用于评估薄板 TED 的尺寸相关表达式。在能量耗散方法的基础上，还导出了包含小尺度效应的 TED 分析表达式。为了调查不同连续介质理论对 TED 的影响，将 SGT 获得的结果与修正偶应力理论 (MCST) 和经典连续介质理论预测的结果进行了比较。此外，