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Thermoelastic Plane Waves in Materials with a Microstructure Based on Micropolar Thermoelasticity with Two Temperature and Higher Order Time Derivatives

Author

Listed:
  • Ahmed E. Abouelregal

    (Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 77455, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Marin Marin

    (Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brașov, Romania)

  • Fahad Alsharari

    (Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 77455, Saudi Arabia)

Abstract

The study of the effect of the microstructure is important and is most evident in elastic vibrations of high frequency and short-wave duration. In addition to deformation caused by temperature and acting forces, the theory of micropolar thermoelasticity is applied to investigate the microstructure of materials when the vibration of their atoms or molecules is increased. This paper addresses a two-dimensional problem involving a thermoelastic micro-polar half-space with a traction-free surface and a known conductive temperature at the medium surface. The problem is treated in the framework of the concept of two-temperature thermoelasticity with a higher-order time derivative and phase delays, which takes into consideration the impact of microscopic structures in non-simple materials. The normal mode technique was applied to find the analytical formulas for thermal stresses, displacements, micro-rotation, temperature changes, and coupled stress. The numerical results are graphed, and the effect of the discrepancy indicator and higher-order temporal derivatives is examined. There are also some exceptional cases that are covered.

Suggested Citation

  • Ahmed E. Abouelregal & Marin Marin & Fahad Alsharari, 2022. "Thermoelastic Plane Waves in Materials with a Microstructure Based on Micropolar Thermoelasticity with Two Temperature and Higher Order Time Derivatives," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1552-:d:808818
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    References listed on IDEAS

    as
    1. Ahmed E. Abouelregal & Marin Marin, 2020. "The Size-Dependent Thermoelastic Vibrations of Nanobeams Subjected to Harmonic Excitation and Rectified Sine Wave Heating," Mathematics, MDPI, vol. 8(7), pages 1-13, July.
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    Cited by:

    1. Osama Moaaz & Ahmed E. Abouelregal & Fahad Alsharari, 2022. "Analysis of a Transversely Isotropic Annular Circular Cylinder Immersed in a Magnetic Field Using the Moore–Gibson–Thompson Thermoelastic Model and Generalized Ohm’s Law," Mathematics, MDPI, vol. 10(20), pages 1-24, October.

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