Memory response in plane wave reflection in generalized magneto-thermoelasticity

ABSTRACT

This paper demonstrates the reflection phenomenon of the magneto-thermoelastic plane waves from a stress-free surface of a homogeneous, isotropic, thermally and electrically conducting solid half-space. We employ the generalized thermoelasticity model with memory-dependent derivative (MDD) for this study. We find that three basic plane waves consisting of two sets of coupled longitudinal waves and one independent shear type wave may travel with distinct speeds in the medium. The speeds of the coupled longitudinal waves are plotted graphically to predict a comparison for the MDD and Lord–Shulman models. At last, for an appropriate material, the reflection coefficients are computed numerically and presented graphically with the angle of incidence of the incident (vertically polarized) shear type wave and the obtained results are explained.

KEYWORDS:

• Memory-dependent derivative
• time-delay
• kernel function
• P- and SV -waves
• dispersion
• reflection

Acknowledgments

The authors would like to gratefully acknowledge the Editor and the reviewer for their constructive and valuable comments and suggestions to improve the quality of the manuscript. They also gratefully acknowledge Professor Samiran Ghosh (Professor, Department of Applied Mathematics, University of Calcutta, Kolkata-700009, India.) for his valuable suggestions in preparing the revised version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Soumen De http://orcid.org/0000-0001-8988-3679

Nantu Sarkar  http://orcid.org/0000-0001-9144-4587

Additional information

Notes on contributors

Nihar Sarkar

Nihar Sarkar received his MSc degree in Applied Mathematics from University of Kalyani, West Bengal, India, in 2005. He is currently an Assistant Professor in Mathematics, City College, Kolkata, India. His research interests include wave propagation in elastic and thermoelastic solids.

Soumen De

Soumen De received his MSc and PhD degrees in Applied Mathematics from University of Calcutta, Kolkata, India in 2004 and 2009, respectively. He is now an Assistant Professor in Applied Mathematics at the Department of Applied Mathematics, University of Calcutta. His research interests include water waves and waves in continuum.

Nantu Sarkar

Nantu Sarkar received his MSc (Applied Mathematics) and PhD (Science) from Jadavpur University, Jadavpur, Kolkata, India in 2008 and 2013, respectively. He is currently an Assistant Professor in Applied Mathematics at the Department of Applied Mathematics, University of Calcutta, Kolkata, India. His research interests include waves in non-local elastic and thermoelastic solids.