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<p>Owing to its dominant role in energy dissipation, thermoelastic damping (TED) must be reliably predicted to facilitate the development of high-performance microbeam resonators. The transition from the Euler–Bernoulli theory (EBT) to higher-order shear deformation theories (HSDTs) increases the versatility of the formulation and enables its application to both slender and thick beam structures. In parallel, micro- and nano-structured elements are known to display marked scale sensitivity in elastic behavior and heat propagation. This work establishes a unified TED framework for shear-deformable microbeams through the coupling diverse HSDTs with scale-sensitive thermo-mechanical formulations. Size dependency in the elastic and thermal responses is introduced through the modified couple stress theory (MCST) and nonlocal dual-phase-lag (NDPL) heat equation. Once the coupled mechanical and thermal equations are formulated and the spatial temperature field is determined, TED can be evaluated via the frequency-based analysis. Besides TED, the study also examines the frequency shift (FS) induced by thermoelastic interactions. The results section showcases multiple numerical scenarios to elucidate how employing HSDTs alongside scale-sensitive frameworks influences TED, FS, and the thermal profile. It is shown that omitting shear effect can introduce errors of several tens of percent in TED estimates, with the discrepancy magnified for thicker beams and higher modes. Accounting for couple stress and thermal nonlocality also suppresses TED.</p>

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A unified analytical framework for thermoelastic damping in microscale resonators: integrating shear deformation beam models with dual mechanical-thermal size dependencies

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Vahid Borjalilou,
  • Shahab Esmaeili,
  • Mohsen Asghari,
  • Ali Mohammad Baghestani,
  • Ali Ebrahimi-Mamaghani

摘要

Owing to its dominant role in energy dissipation, thermoelastic damping (TED) must be reliably predicted to facilitate the development of high-performance microbeam resonators. The transition from the Euler–Bernoulli theory (EBT) to higher-order shear deformation theories (HSDTs) increases the versatility of the formulation and enables its application to both slender and thick beam structures. In parallel, micro- and nano-structured elements are known to display marked scale sensitivity in elastic behavior and heat propagation. This work establishes a unified TED framework for shear-deformable microbeams through the coupling diverse HSDTs with scale-sensitive thermo-mechanical formulations. Size dependency in the elastic and thermal responses is introduced through the modified couple stress theory (MCST) and nonlocal dual-phase-lag (NDPL) heat equation. Once the coupled mechanical and thermal equations are formulated and the spatial temperature field is determined, TED can be evaluated via the frequency-based analysis. Besides TED, the study also examines the frequency shift (FS) induced by thermoelastic interactions. The results section showcases multiple numerical scenarios to elucidate how employing HSDTs alongside scale-sensitive frameworks influences TED, FS, and the thermal profile. It is shown that omitting shear effect can introduce errors of several tens of percent in TED estimates, with the discrepancy magnified for thicker beams and higher modes. Accounting for couple stress and thermal nonlocality also suppresses TED.