Viscoelastic Pasternak foundation analysis of a thermoelastic microbeam using Moore–Gibson–Thompson heat conduction under Klein–Gordon (KG) nonlocality

Ahmed Yahya; Adam Zakria; Ibrahim-Elkhalil Ahmed; Shams A. Ahmed; Husam E. Dargail; Abdelgabar Adam Hassan; Eshraga Salih; Ahmed Yahya; Adam Zakria; Ibrahim-Elkhalil Ahmed; Shams A. Ahmed; Husam E. Dargail; Abdelgabar Adam Hassan; Eshraga Salih

doi:10.3934/math.2025471

AIMS Mathematics

2025, Volume 10, Issue 5: 10340-10358. doi: 10.3934/math.2025471

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Viscoelastic Pasternak foundation analysis of a thermoelastic microbeam using Moore–Gibson–Thompson heat conduction under Klein–Gordon (KG) nonlocality

1.
Department of Mathematics, College of Science, Jouf University, Sakaka, 2014, Saudi Arabia
2.
Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia

Received: 10 December 2024 Revised: 19 April 2025 Accepted: 29 April 2025 Published: 06 May 2025
MSC : 74-10, 74B05, 74F05, 74H15

This study sought to examine the behavior of thermoelastic microbeams supported by a viscoelastic Pasternak foundation via the Moore–Gibson–Thompson heat conduction equation within the framework of Klein–Gordon nonlocality, a novel approach for analyzing heat transfer in elastic materials. This model facilitates a more precise comprehension of the thermoelastic vibrations in microbeams. We wanted to examine the impact of foundation characteristics and thermal relaxation durations on the vibration frequency and stability of the microbeam. The Laplace transform technique was used. A graphic representation of the computed temperature, bending displacement, and moment is shown. The results provide significant insights into the design and enhancement of microbeams in advanced engineering applications, including microelectromechanical systems and nanoscale structures, where temperature effects and foundational interactions are critical. Furthermore, the fluctuation of waves is somewhat reduced in the examined model.
- thermoelastic,
- Klein–Gordon nonlocality,
- microbeams,
- foundation,
- viscoelastic,
- Pasternak foundation,
- Moore–Gibson–Thompson
Citation: Ahmed Yahya, Adam Zakria, Ibrahim-Elkhalil Ahmed, Shams A. Ahmed, Husam E. Dargail, Abdelgabar Adam Hassan, Eshraga Salih. Viscoelastic Pasternak foundation analysis of a thermoelastic microbeam using Moore–Gibson–Thompson heat conduction under Klein–Gordon (KG) nonlocality[J]. AIMS Mathematics, 2025, 10(5): 10340-10358. doi: 10.3934/math.2025471

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Abstract

This study sought to examine the behavior of thermoelastic microbeams supported by a viscoelastic Pasternak foundation via the Moore–Gibson–Thompson heat conduction equation within the framework of Klein–Gordon nonlocality, a novel approach for analyzing heat transfer in elastic materials. This model facilitates a more precise comprehension of the thermoelastic vibrations in microbeams. We wanted to examine the impact of foundation characteristics and thermal relaxation durations on the vibration frequency and stability of the microbeam. The Laplace transform technique was used. A graphic representation of the computed temperature, bending displacement, and moment is shown. The results provide significant insights into the design and enhancement of microbeams in advanced engineering applications, including microelectromechanical systems and nanoscale structures, where temperature effects and foundational interactions are critical. Furthermore, the fluctuation of waves is somewhat reduced in the examined model.

References

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