 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13427 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8178
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| In English (Mech. Solids): | | 5249 |
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| P.P. Bhad, V.R. Manthena, A.M. Shende, N.K. Lamba, I. Abbas, and A. Almuneef, "Thermoelastic Behaviour of a Fractional Ordered Thermosensitive Functionally Graded Elliptical Plate due to Laser Heating," Mech. Solids. 60 (6), 4801-4817 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
6 |
Pages |
4801-4817 |
| DOI |
10.1134/S0025654425603611 |
| Title |
Thermoelastic Behaviour of a Fractional Ordered Thermosensitive Functionally Graded Elliptical Plate due to Laser Heating |
| Author(s) |
P.P. Bhad (Department of Mathematics, Priyadarshini J.L. College of Engineering, Nagpur, India, praash.bhad@gmail.com)
V.R. Manthena (Department of Mathematics, Priyadarshini J.L. College of Engineering, Nagpur, India, vkmanthena@gmail.com)
A.M. Shende (Principal, Priyadarshini J.L. College of Engineering, Nagpur, India, shende_renu@yahoo.com)
N.K. Lamba (Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Mandhal, Nagpur, India, navneetkumarlamba@gmail.com)
I. Abbas (Mathematics Department, Faculty of Science, Sohag University, Egypt, ibrabbas7@science.sohag.edu.eg)
A. Almuneef (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, P.O. Box 84428, 11671 Saudi Arabia, aaalmuneef@pnu.edu.sa) |
| Abstract |
We derive the time fractional heat conduction equation (FHCE) for a functionally graded
elliptical annulus plate using non-Fourier heat conduction principles that account for memory effects
rather than instantaneous responses, influenced by a moving laser heat source. Thermal conductivity,
heat capacity, and density are presumed to vary axially and depend on temperature. The upper and
lower plates are at zero, while Biot criteria and the Kirpichev reference number for convection energy
transfer boundaries regulate the geometrically curved areas. Kirchhoff’s variable transformation linearises the FHCE governing the given conditions. The heat equation is resolved through the application of the Laplace transform, modified Mathieu transform, and Taylor series, followed by their inversions. The inverse of Kirchhoff’s Laplace domain transformation establishes the temperature distribution. Numerical analyses of titanium carbide and nickel properties yielded graphs depicting
temperature, motion, and stress variations during laser pulse duration and velocity. |
| Keywords |
Functionally graded elliptic plate, thermosensitive, fractional, laser heat, temperature, stresses, integral transform |
| Received |
02 July 2025 | Revised |
09 August 2025 | Accepted |
09 August 2025 |
| Link to Fulltext |
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