<p>Considering the critical role of thermoelastic dissipation (TED) in ultra-small resonators and the strong influence of size on mechanical and thermal fields, this study develops a new analytical framework for TED and frequency shift (FS) in miniature circular plates through the frequency-based method. Scale effects are incorporated into the governing equations through the modified couple stress theory (MCST) and the nonlocal dual-phase-lag (NDPL) heat transfer model. The complex frequency of the plate is decomposed into its real and imaginary components using the frequency-based method, leading to a monomial relationship for TED, influenced by the specific constants in MCST and NDPL heat equation. To assess the reliability of the model, its outcomes are benchmarked against those reported in prior investigations. The study also conducts a parametric investigation to examine how TED and FS vary with key parameters, including the MCST characteristic length, thermal nonlocal parameter, plate geometry, vibration mode, support conditions and material properties. The findings suggest that the developed scale-dependent approach, using MCST and NDPL models, approximates a generally lower TED value than that of the classical approach based on the classical continuum theory (CCT) and the Fourier law.</p>

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Scale-dependent simulation of nonlocal dual-phase-lag thermoelastic dissipation and frequency shift in circular nanoplate resonators via the frequency-based method

  • Abdulilah Mohammad Mayet,
  • Salman Arafath Mohammed,
  • Shamimul Qamar,
  • Neeraj Kumar Shukla,
  • Mohammed Abdul Muqeet

摘要

Considering the critical role of thermoelastic dissipation (TED) in ultra-small resonators and the strong influence of size on mechanical and thermal fields, this study develops a new analytical framework for TED and frequency shift (FS) in miniature circular plates through the frequency-based method. Scale effects are incorporated into the governing equations through the modified couple stress theory (MCST) and the nonlocal dual-phase-lag (NDPL) heat transfer model. The complex frequency of the plate is decomposed into its real and imaginary components using the frequency-based method, leading to a monomial relationship for TED, influenced by the specific constants in MCST and NDPL heat equation. To assess the reliability of the model, its outcomes are benchmarked against those reported in prior investigations. The study also conducts a parametric investigation to examine how TED and FS vary with key parameters, including the MCST characteristic length, thermal nonlocal parameter, plate geometry, vibration mode, support conditions and material properties. The findings suggest that the developed scale-dependent approach, using MCST and NDPL models, approximates a generally lower TED value than that of the classical approach based on the classical continuum theory (CCT) and the Fourier law.