Exploration of exact wave solutions for the Lord-Shulman thermo-elasticity theory with temperature dependence using advanced techniques

Mohamed F. Ismail; Hamdy M. Ahmed; Alaa A. El-Bary; Hamdy M. Youssef; Islam Samir; Mohamed F. Ismail; Hamdy M. Ahmed; Alaa A. El-Bary; Hamdy M. Youssef; Islam Samir

doi:10.3934/math.2025491

AIMS Mathematics

2025, Volume 10, Issue 5: 10806-10830. doi: 10.3934/math.2025491

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Exploration of exact wave solutions for the Lord-Shulman thermo-elasticity theory with temperature dependence using advanced techniques

1.
Faculty of Computers and Information System, Egyptian Chinese University, Cairo, Egypt
2.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt
3.
Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt
4.
National Committee for Mathematics, Academy of Scientific Research and Technology, Egypt
5.
Council of Future Studies and Risk Management, Academy of Scientific Research and Technology, Egypt
6.
Mechanical Engineering Department, College of Engineering and Architecture, Umm Al-Qura University, Makkah 21955, Saudi Arabia
7.
Department of Mathematics and Engineering Physics, Faculty of Engineering, Aim Shams University, Cairo, Egypt

Received: 05 February 2025 Revised: 06 May 2025 Accepted: 07 May 2025 Published: 12 May 2025
MSC : 74B20, 35C05, 35C07, 35C08

This study sought to improve the comprehension of wave propagation in thermo-elastic materials according to Lord-Shulman (L-S) theory by developing precise wave solutions for the governing equations that take into consideration temperature-dependent material features. The research utilized the improved simple equation method (ISEM) to analyze the interrelated thermal and mechanical properties of these materials, allowing the creation of analytical solutions that exactly characterize intricate wave processes. The ISEM facilitates the development of various wave shapes. These solutions, defined by configurable free parameters, offer a flexible framework for examining diverse physical circumstances in thermo-elasticity. The work includes detailed graphical representations of crucial discoveries such as temperature distributions, stress tensors, and displacement which provide amazing visual insights into the complex interactions that occur within thermo-elastic systems.
- nonlinear thermo-elasticity,
- temperature-dependence,
- analytical wave solutions
Citation: Mohamed F. Ismail, Hamdy M. Ahmed, Alaa A. El-Bary, Hamdy M. Youssef, Islam Samir. Exploration of exact wave solutions for the Lord-Shulman thermo-elasticity theory with temperature dependence using advanced techniques[J]. AIMS Mathematics, 2025, 10(5): 10806-10830. doi: 10.3934/math.2025491

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Abstract

This study sought to improve the comprehension of wave propagation in thermo-elastic materials according to Lord-Shulman (L-S) theory by developing precise wave solutions for the governing equations that take into consideration temperature-dependent material features. The research utilized the improved simple equation method (ISEM) to analyze the interrelated thermal and mechanical properties of these materials, allowing the creation of analytical solutions that exactly characterize intricate wave processes. The ISEM facilitates the development of various wave shapes. These solutions, defined by configurable free parameters, offer a flexible framework for examining diverse physical circumstances in thermo-elasticity. The work includes detailed graphical representations of crucial discoveries such as temperature distributions, stress tensors, and displacement which provide amazing visual insights into the complex interactions that occur within thermo-elastic systems.

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