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Thermoelastic damping in micro/nano-plate vibrations: 3D modeling using modified couple stress theory and the Moore–Gibson–Thompson equation

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Abstract

This paper introduces a size-dependent model for evaluating thermoelastic damping (TED) in small-scaled rectangular plates, incorporating three-dimensional (3D) heat transfer. Utilizing the modified couple stress theory (MCST) and Moore–Gibson–Thompson (MGT) heat equation, we enhance the thermomechanical analysis accuracy in micro/nano-structures. The model employs MCST to derive size-dependent constitutive relations for rectangular plates, coupled with the MGT model for formulating the 3D heat conduction equation. This approach facilitates the analysis of the 3D temperature field and aids in defining TED using the energy loss method. Consequently, an analytical expression is developed to predict 3D TED in rectangular plate resonators, integrating characteristic MCST length and nonclassical MGT parameters. Comparative analyses with existing studies and a series of simulated numerical results are presented. These simulations primarily focus on contrasting the 3D model with conventional 1D models and examining the effects of implementing MCST and MGT models. Findings reveal that the proposed formulation significantly alters outcomes for very small and relatively thick plates compared to simpler models. This advancement in modeling provides a more precise understanding of TED in micro/nano-plate structures, offering vital insights for their optimal design and application in advanced technological fields.

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Acknowledgements

The authors would like to thank the Researchers Supporting Project number (RSPD2024R993), King Saud University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. King Abdullah Institute for Nanotechnology, King Saud University, Riyadh, 11451, Saudi Arabia

    Khalid Mujasam Batoo

  2. Department of Medical Laboratories Technology, Al-Manara College for Medical Sciences, Maysan, Iraq

    Shaymaa Abed Hussein

  3. Department of Construction Engineering & Project Management, Al-Noor University College, Nineveh, Iraq

    Ehab Essam Aziz

  4. College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq

    Manal Morad Karim

  5. Department of Medical Engineering, Al-Hadi University College, Baghdad, 10011, Iraq

    Ayadh Al-khalidi

  6. Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

    Ahmed Ahmed Ibrahim

  7. Department of Engineering & Physics, Southern Arkansas University, Magnolia, AR, 71753, USA

    Bouchaib Zazoum

  8. College of Dentistry, Al-Ayen University, Thi-Qar, Iraq

    Montather F. Ramadan

  9. Department of Medical Laboratories Technology, AL-Nisour University College, Baghdad, Iraq

    Jamal K. Abbas

  10. College of Technical Engineering, The Islamic University, Najaf, Iraq

    Ahmed Elawady

  11. College of Technical Engineering, The Islamic University of Al Diwaniyah, Al-Qadisiyah, Iraq

    Ahmed Elawady

  12. College of Technical Engineering, The Islamic University of Babylon, Babylon, Iraq

    Ahmed Elawady

  13. Department of Mechanical Engineering, Faculty of Engineering, University of Kufa, Kufa, Iraq

    Ghassan Fadhil Smaisim

  14. Nanotechnology and Advanced Materials Research Unit (NAMRU), Faculty of Engineering, University of Kufa, Kufa, Iraq

    Ghassan Fadhil Smaisim

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  1. Khalid Mujasam Batoo
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Contributions

Khalid Mujasam Batoo did Project administration and Software. Shaymaa Abed Hussein did Writing and Visualization. Ehab Essam Aziz performed Investigation and Software. Manal Morad Karim conducted Formal analysis and Writing. Ayadh Al-khalidi did Writing and Visualization. Ahmed Ahmed Ibrahim carried out Visualization and Validation. Bouchaib Zazoum did Writing and Visualization. Montather F. Ramadan performed Investigation and Software. Jamal K. Abbas did Writing and Data curation. Ahmed Elawady did Writing and Software. Ghassan Fadhil Smaisim carried out Supervision and Validation.

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Correspondence to Ghassan Fadhil Smaisim.

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Mujasam Batoo, K., Hussein, S.A., Aziz, E.E. et al. Thermoelastic damping in micro/nano-plate vibrations: 3D modeling using modified couple stress theory and the Moore–Gibson–Thompson equation. Mech Time-Depend Mater (2024). https://doi.org/10.1007/s11043-024-09680-w

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