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Viscothermoelastic vibrations on circular microplate resonators using the Moore–Gibson–Thompson thermal-conductivity model

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Abstract

This research investigates the impact of thermoelastic coupling on thermally conducting, homogeneous, and isotropic Kelvin–Voigt-type circular microplate resonators. The study utilizes the Moore–Gibson–Thompson technique, which incorporates viscous effects. We examine the use of clamped boundary conditions and obtain analytical solutions in the Laplace-transform domain. In order to clarify the thermomechanical effects on the vibrations of a ceramic Si3N4 plate resonator, we calculate numerical outcomes in the time domain by employing the inverse Laplace transform. We examine the impact of viscosity on many physical phenomena, including deflection, temperature, displacement, thermal moment in the radial direction, and radial stress. We give graphical findings that compare the results with and without the presence of viscosity. The study evaluates the precision and feasibility of the MGTE thermal-conductivity theory by comparing its numerical outcomes with well-established thermoelastic models, such as the classical theory, Lord–Shulman theory, and Green–Naghdi II and III theories. The MGTE theory showcases improved accuracy, facilitating the production of circular micro/nanoplate resonators with exceptional quality and decreased energy dissipation.

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Authors and Affiliations

  1. Department of Mathematics, Nitishwar College, Constituent unit of Babasaheb Bhimrao Ambedkar Bihar University, Muzaffarpur, Bihar, 842002, India

    Rakhi Tiwari

  2. Department of Mathematics, Central University of South Bihar, Gaya, Bihar, India

    Satyam Sachan & Roushan Kumar

  3. Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia

    Ahmed Abouelregal

  4. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Ahmed Abouelregal & Mohamed E. Elzayady

Authors
  1. Rakhi Tiwari
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  2. Satyam Sachan
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  3. Ahmed Abouelregal
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  4. Roushan Kumar
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  5. Mohamed E. Elzayady
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Contributions

R.T. gave the idea and constructed mathematical models and written the complete manuscript. S.S., A.A., R.K. worked on software and prepared graphs. M.E. helped in revising the manuscript.

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Correspondence to Rakhi Tiwari.

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Tiwari, R., Sachan, S., Abouelregal, A. et al. Viscothermoelastic vibrations on circular microplate resonators using the Moore–Gibson–Thompson thermal-conductivity model. Mech Time-Depend Mater (2024). https://doi.org/10.1007/s11043-024-09699-z

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