Nonlocal Harmonically Varying Heat in a Magneto-Thermoelastic Thick Plate Using Simple and Refined Lord and Shulman Theories

This work presents a solution to the nonlocal harmonically varying heat model in a magneto-thermoelastic thick plate. The classical, simple, and refined Lord and Shulman theories of thermoelasticity are applied. The medium is under a harmonic varying heat source with a constant strength and applied...

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Main Authors: Ashraf M. Zenkour, Maryam H. Aljadani
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/7/1160
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author Ashraf M. Zenkour
Maryam H. Aljadani
author_facet Ashraf M. Zenkour
Maryam H. Aljadani
author_sort Ashraf M. Zenkour
collection DOAJ
description This work presents a solution to the nonlocal harmonically varying heat model in a magneto-thermoelastic thick plate. The classical, simple, and refined Lord and Shulman theories of thermoelasticity are applied. The medium is under a harmonic varying heat source with a constant strength and applied longitudinal magnetic field. Additionally, the nonlocal effect of thermoelastic materials is demonstrated using Eringen’s nonlocal theory. The Laplace transform technique is used to find the analytical solution. The numerical inversion approach of the Laplace transform is employed to determine the solution within the physical domain. The impacts of nonlocal, time parameters, and the angular frequency of thermal vibration on the field variables are presented graphically and analyzed in detail. The findings indicate that the responses of the magneto-thermoelastic thick plate to harmonically varying heat are significantly influenced by each one of the physical parameters. The refined Lord and Shulman model presents significant fluctuations in the results due to the theory’s additional terms.
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spelling doaj-art-71d1c406b9e448c2bafa33642954b9272025-08-20T02:17:00ZengMDPI AGMathematics2227-73902025-03-01137116010.3390/math13071160Nonlocal Harmonically Varying Heat in a Magneto-Thermoelastic Thick Plate Using Simple and Refined Lord and Shulman TheoriesAshraf M. Zenkour0Maryam H. Aljadani1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Jamoum University Collage, Umm Al-Qura University, Makkah 21421, Saudi ArabiaThis work presents a solution to the nonlocal harmonically varying heat model in a magneto-thermoelastic thick plate. The classical, simple, and refined Lord and Shulman theories of thermoelasticity are applied. The medium is under a harmonic varying heat source with a constant strength and applied longitudinal magnetic field. Additionally, the nonlocal effect of thermoelastic materials is demonstrated using Eringen’s nonlocal theory. The Laplace transform technique is used to find the analytical solution. The numerical inversion approach of the Laplace transform is employed to determine the solution within the physical domain. The impacts of nonlocal, time parameters, and the angular frequency of thermal vibration on the field variables are presented graphically and analyzed in detail. The findings indicate that the responses of the magneto-thermoelastic thick plate to harmonically varying heat are significantly influenced by each one of the physical parameters. The refined Lord and Shulman model presents significant fluctuations in the results due to the theory’s additional terms.https://www.mdpi.com/2227-7390/13/7/1160nonlocal elasticitythermal vibrationharmonically varying heatsimple and refined LS theories
spellingShingle Ashraf M. Zenkour
Maryam H. Aljadani
Nonlocal Harmonically Varying Heat in a Magneto-Thermoelastic Thick Plate Using Simple and Refined Lord and Shulman Theories
Mathematics
nonlocal elasticity
thermal vibration
harmonically varying heat
simple and refined LS theories
title Nonlocal Harmonically Varying Heat in a Magneto-Thermoelastic Thick Plate Using Simple and Refined Lord and Shulman Theories
title_full Nonlocal Harmonically Varying Heat in a Magneto-Thermoelastic Thick Plate Using Simple and Refined Lord and Shulman Theories
title_fullStr Nonlocal Harmonically Varying Heat in a Magneto-Thermoelastic Thick Plate Using Simple and Refined Lord and Shulman Theories
title_full_unstemmed Nonlocal Harmonically Varying Heat in a Magneto-Thermoelastic Thick Plate Using Simple and Refined Lord and Shulman Theories
title_short Nonlocal Harmonically Varying Heat in a Magneto-Thermoelastic Thick Plate Using Simple and Refined Lord and Shulman Theories
title_sort nonlocal harmonically varying heat in a magneto thermoelastic thick plate using simple and refined lord and shulman theories
topic nonlocal elasticity
thermal vibration
harmonically varying heat
simple and refined LS theories
url https://www.mdpi.com/2227-7390/13/7/1160
work_keys_str_mv AT ashrafmzenkour nonlocalharmonicallyvaryingheatinamagnetothermoelasticthickplateusingsimpleandrefinedlordandshulmantheories
AT maryamhaljadani nonlocalharmonicallyvaryingheatinamagnetothermoelasticthickplateusingsimpleandrefinedlordandshulmantheories