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<p>Energy loss due to thermoelastic damping (TED) is a primary limitation on the performance of micro/nanoscale resonators, making precise prediction of this phenomenon vital for optimizing the quality factor and long-term stability of nanoelectromechanical devices. The adoption of higher-order shear deformation theories (HSDTs) enables more refined modeling and accommodates a wider variety of beam geometries. Additionally, traditional formulations disregard the strong size-dependent features that dominate structural and thermal behavior at reduced dimensions. This study establishes a unified approach for analyzing TED in nanoscale beams within the context of various HSDTs, highlighting the concurrent consideration of structural and thermal size effects. Structural size dependence is captured via nonlocal elasticity theory (NET), while thermal size effects are described using the dual-phase-lag (DPL) heat conduction model. The analysis yields governing relations that explicitly include size effects. The complex natural frequency is decomposed into its real and imaginary components, and the frequency-domain approach is employed to formulate the TED expression. The framework is first benchmarked against existing results to ensure consistency, after which detailed simulations are provided. Comparative results reveal that HSDTs provide markedly different TED characterizations for moderately thick and thick beams compared to the Euler–Bernoulli theory (EBT), reinforcing their relevance in high-fidelity resonator analysis.</p>

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Mathematical formulation for thermoelastic damping in nonlocal shear deformable beams incorporating dual-phase-lag heat conduction

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Suleiman Ibrahim Mohammad,
  • Sabir Widatalla,
  • Asokan Vasudevan,
  • Lamees M. Hassan,
  • S Sujai,
  • Akanksha Mishra,
  • I. B. Sapaev,
  • Shahbaz Juneja,
  • Premananda Pradhan,
  • S. P. Venkatesan

摘要

Energy loss due to thermoelastic damping (TED) is a primary limitation on the performance of micro/nanoscale resonators, making precise prediction of this phenomenon vital for optimizing the quality factor and long-term stability of nanoelectromechanical devices. The adoption of higher-order shear deformation theories (HSDTs) enables more refined modeling and accommodates a wider variety of beam geometries. Additionally, traditional formulations disregard the strong size-dependent features that dominate structural and thermal behavior at reduced dimensions. This study establishes a unified approach for analyzing TED in nanoscale beams within the context of various HSDTs, highlighting the concurrent consideration of structural and thermal size effects. Structural size dependence is captured via nonlocal elasticity theory (NET), while thermal size effects are described using the dual-phase-lag (DPL) heat conduction model. The analysis yields governing relations that explicitly include size effects. The complex natural frequency is decomposed into its real and imaginary components, and the frequency-domain approach is employed to formulate the TED expression. The framework is first benchmarked against existing results to ensure consistency, after which detailed simulations are provided. Comparative results reveal that HSDTs provide markedly different TED characterizations for moderately thick and thick beams compared to the Euler–Bernoulli theory (EBT), reinforcing their relevance in high-fidelity resonator analysis.