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A Phase Delay Thermoelastic Model with Higher Derivatives and Two Temperatures for the Hall Current Effect on a Micropolar Rotating Material

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Abstract

Purpose

As the micropolar thermoelasticity theory predicted, flexible materials can experience significant vibration, temperature variations, and microrotations due to transitional and rotational motions. This study presents a new micropolar thermoelasticity theory with a two-phase delay of high-order and two temperatures. The proposed model has been used to study the microstructure of rotating materials when their atomic or molecular vibrations change under the effects of Hall current. There is an assumption that the angular velocity of an elastic medium is always the same.

Methods

The proposed problem was solved and analyzed using the normal mode approach. For the purpose of analysis and comparison, the theoretical results of deformations, temperatures, and other fields are provided and graphically depicted.

Results and Conclusions

The results showed that the higher-order phase delays and the two-temperature factor significantly affected the behavior of all studied variables.

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Data Availability

The authors confirm that the article data supporting the conclusions of this study are included within the paper.

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Acknowledgements

The authors thank the Deanship of Scientific Research at Jouf University for funding this work through research grant no. DSR2022-RG-0137. We would also like to extend our sincere thanks to the College of Science and Arts in Al-Qurayyat for its technical support.

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayat, 77455, Saudi Arabia

    Ahmed E. Abouelregal, Khalil M. Khalil & Mohamed E. Nasr

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

    Osama Moaaz

  3. Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah, 51482, Saudi Arabia

    Osama Moaaz

  4. Department of Computational Mathematics, Science, and Engineering (CMSE), College of Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Mohamed Abouhawwash

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  1. Ahmed E. Abouelregal
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  3. Khalil M. Khalil
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Correspondence to Ahmed E. Abouelregal.

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Abouelregal, A.E., Moaaz, O., Khalil, K.M. et al. A Phase Delay Thermoelastic Model with Higher Derivatives and Two Temperatures for the Hall Current Effect on a Micropolar Rotating Material. J. Vib. Eng. Technol. 12, 1505–1523 (2024). https://doi.org/10.1007/s42417-023-00922-8

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