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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/7/1160 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850184551336247296 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-71d1c406b9e448c2bafa33642954b927 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| 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 |