Abstract
The Lord-Shulman theory of generalized thermoelasticity based on a memory-dependent derivative is employed to study the propagation of plane harmonic waves in a two-dimensional semi-infinite thermoelastic medium. The numerical solution is analyzed for various values of the time delay parameter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I. Podlubny, Fractional Differential Equations (Academic Press, New York, 1999).
N. Sarkar, “Wave Propagation in an Initially Stressed Elastic Half-Space Solids under Time-Fractional Order Two-Temperature Magneto-Thermoelasticity,” Eur. Phys. J. Plus. 132, 154–167 (2017).
N. Sarkar and Kh. Lotfy, “A 2D Problem of Time-Fractional Heat Order for Two-Temperature Thermoelasticity under Hydrostatic Initial Stress,” Mech. Adv. Mater. Structures 25, 279–285 (2018).
M. A. Ezzat, A. S. El-Karamany, A. A. El-Bary, and M. Fayik, “Fractional Ultrafast-Laser-Induced Magneto-Thermoelastic Behavior in Perfect Conducting Metal Films,” J. Electromagnet. Waves Appl. 28, 64–82 (2014).
M. Bachher, N. Sarkar, and A. Lahiri, “Generalized Thermoelastic Infinite Medium with Voids Subjected to a Instantaneous Heat Sources with Fractional Derivative Heat Transfer,” Int. J. Mech. Sci. 89, 84–91 (2014).
J. Wang and H. Li, “Surpassing the Fractional Derivative: Concept of the Memory-Dependent Derivative,” Comput. Math. Appl. 62, 1562–1567 (2011).
Y.-J. Yu, W. Hu., and X.-G. Tian, “A Novel Generalized Thermoelasticity Model Based on Memory-Dependent Derivative,” Int. J. Eng. Sci. 81, 23–134 (2014).
H. W. Lord and Y. A. Shulman, “Generalized Dynamical Theory of Thermoelasticity,” J. Mech. Phys. Solids 15, 299–309 (1967).
M. A. Ezzat, A. S. El-Karamany, and A. A. El-Bary, “Generalized Thermo-Viscoelasticity with Memory Dependent Derivatives,” Int. J. Mech. Sci. 89, 470–475 (2014).
M. A. Ezzat, A. S. El-Karamany, and M. A. Ezzat, A. S. El-Karamany, and A. A. El-Bary, “A Novel Magneto Thermoelasticity Theory with Memory Dependent Derivative,” J. Electromagnet. Waves Appl. 29, 1018–1031 (2015).
M. A. Ezzat, A. S. El-Karamany, and A. A. El-Bary, “Generalized Thermoelasticity with Memory-Dependent Derivatives Involving Two-Temperatures,” Mech. Adv. Mat. Struct. 23, 545–553 (2016).
Kh. Lotfy and N. Sarkar, “Memory-Dependent Derivatives for Photothermal Semiconducting Medium in Generalized Thermoelasticity with Two-Temperature,” Mech. Time-Dependent. Materials 21, 519–534 (2017).
N. Sarkar and A. Lahiri, “A Three-Dimensional Thermoelastic Problem for a Half-Space without Energy Dissipation,” Int. J. Engng Sci. 51, 310–325 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M. Bachher.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 60, No. 1, pp. 142–151, January–February, 2019.
Rights and permissions
About this article
Cite this article
Bachher, M. Plane Harmonic Waves in Thermoelastic Materials with a Memory-Dependent Derivative. J Appl Mech Tech Phy 60, 123–131 (2019). https://doi.org/10.1134/S0021894419010152
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894419010152