Abstract An explicit formula of coupled three-phase-lag (TPL) thermoelasticity theory under the Timoshenko beam is constructed for microbeam resonators. The constructed mathematical model is based on the modified couple stress theory which implies a prediction of size-dependent effects in microbeam resonators. By using Hamilton’s principle, governing equations for motion and boundary conditions are derived. The thermal moment and thermal deflection of microbeam resonators are studied analytically and numerically. A comparison of the results between modified coupled stress theory and classical theory is executed for TPL, GN-II, and Lord–Shulman (LS) models. Also, a comparison of the results between TPL, GN-II, and LS models for modified coupled stress theory is done. Besides, the result is presented for silicon microbeam for different aspect ratios and phase-lags. It demonstrated the result corresponding to the behavior of thermoelastic frequencies of microbeam resonators.

中文翻译：

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相位滞后对铁木辛哥梁热弹性振动的影响

摘要 构造了Timoshenko 梁下耦合三相滞后(TPL) 热弹性理论的显式公式，用于微梁谐振器。所构建的数学模型基于修正的偶应力理论，该理论意味着对微梁谐振器中尺寸相关效应的预测。通过使用哈密顿原理，推导出运动和边界条件的控制方程。分析和数值研究了微梁谐振器的热力矩和热偏转。对 TPL、GN-II 和 Lord-Shulman (LS) 模型进行了修正耦合应力理论和经典理论之间的结果比较。此外，还对修正耦合应力理论的 TPL、GN-II 和 LS 模型的结果进行了比较。除了，结果显示为不同纵横比和相位滞后的硅微束。它证明了与微梁谐振器的热弹性频率行为相对应的结果。