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Purpose <p>As thermoelastic damping (TED) constitutes the major energy loss pathway in micro/nano-structures, reliable description becomes critical for performance-optimized designs. Successful TED quantification in micro/nano-ring resonators hinges on combining two-dimensional (2D) thermal analysis with size-sensitive mechanical and heat conduction formulations. By employing the modified couple stress theory (MCST) and the Moore-Gibson-Thompson (MGT) heat transfer model, this study constructs a theoretical model for TED in out-of-plane vibrations of rectangular cross-sectional micro/nano-rings subjected to 2D thermal conduction.</p> Methods <p>The analysis begins by deriving the 2D MGT heat equation, followed by determination of the corresponding temperature field. The methodology proceeds by deriving the MCST-based constitutive relations for rectangular cross-sectional rings. The energy-based approach is ultimately used to achieve a size-sensitive TED formula for micro/nano-rings undergoing out-of-plane vibrations with 2D heat transfer considerations.</p> Results and Conclusions <p>Once validated against previous works, the framework is applied in numerical simulations to examine both the variations between 1 and 2D modeling and the significance of size-sensitive thermo-mechanical behavior. Data conclusively show that dimensional effects cannot be neglected at small scales, and simplified 1D approach becomes inadequate for higher vibration modes.</p>

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Thermoelastic Damping in Out-of-Plane Motions of Rectangular Cross-Sectional Rings: A 2D Approach Incorporating Couple Stress Effect and Moore-Gibson-Thompson Thermoelasticity

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Ali Kamil Kareem,
  • Rahul Pradhan,
  • Sabir Widatalla,
  • Mohammed Al-Farouni,
  • Ashutosh Pattanaik,
  • J. Jayaprabakar,
  • Harjot Singh Gill,
  • Pragyan Senapati,
  • M. A. Diab,
  • M. K. Sharma

摘要

Purpose

As thermoelastic damping (TED) constitutes the major energy loss pathway in micro/nano-structures, reliable description becomes critical for performance-optimized designs. Successful TED quantification in micro/nano-ring resonators hinges on combining two-dimensional (2D) thermal analysis with size-sensitive mechanical and heat conduction formulations. By employing the modified couple stress theory (MCST) and the Moore-Gibson-Thompson (MGT) heat transfer model, this study constructs a theoretical model for TED in out-of-plane vibrations of rectangular cross-sectional micro/nano-rings subjected to 2D thermal conduction.

Methods

The analysis begins by deriving the 2D MGT heat equation, followed by determination of the corresponding temperature field. The methodology proceeds by deriving the MCST-based constitutive relations for rectangular cross-sectional rings. The energy-based approach is ultimately used to achieve a size-sensitive TED formula for micro/nano-rings undergoing out-of-plane vibrations with 2D heat transfer considerations.

Results and Conclusions

Once validated against previous works, the framework is applied in numerical simulations to examine both the variations between 1 and 2D modeling and the significance of size-sensitive thermo-mechanical behavior. Data conclusively show that dimensional effects cannot be neglected at small scales, and simplified 1D approach becomes inadequate for higher vibration modes.