Reflection and refraction phenomena of shear horizontal waves at the interfaces of sandwiched anisotropic magnetoelastic
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Reflection and refraction phenomena of shear horizontal waves at the interfaces of sandwiched anisotropic magnetoelastic medium with corrugated boundaries Shishir Gupta1, Snehamoy Pramanik1,a
, Smita1, Arun Kumar Verma2
1 Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines),
Dhanbad 826004, India
2 Department of Mathematics, Hampton University, Hampton, USA
Received: 18 January 2020 / Accepted: 8 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The present article analyses the reflection and refraction phenomena of an incident shear horizontal wave at the lower interface of corrugated anisotropic magnetoelastic medium sandwiched between an upper self-reinforced half-space and a lower heterogeneous viscoelastic half-space. Rayleigh’s approximation method and Snell’s law are employed to obtain an algebraic equation, which is solved by the application of Cramer’s method to determine the reflection and refraction coefficients for the reflected and refracted shear horizontal waves up to first order. The boundary conditions involve the continuity of displacements and stresses at the lower and upper common corrugated interfaces of the sandwiched anisotropic magnetoelastic medium. The deduced reflection and refraction coefficients depend on various parameters, viz. width of the sandwiched layer, anisotropic magnetoelastic constants, heterogeneity parameter, viscoelastic parameter and wave number. These reflected and transmitted coefficients are computed numerically, and their variation due to the affecting parameters is illustrated graphically against angle of incidence. The critical angle and slowness section are also determined for the shear horizontal wave propagating in the considered medium. Moreover, magnitude of energy distributed among each of the reflected and refracted waves is also computed. As a special case, the obtained results are found in well agreement with the pre-established results existing in the literature.
1 Introduction The phenomena of reflection and transmission of seismic waves have been cynosure to the researchers and scientists of various disciplines such as seismology, earthquake engineering and geophysics. These analyses impart a great deal of information about the Earth’s interior and its composition. The data collected from the analysis of reflected and transmitted waves are significantly utilised in the domain of mining and fuel engineering for the purpose of exploration of minerals and fuels such as rocks, oils, gases and hydrocarbons. The results of the analysis of reflected and refracted waves also extend their domain of application in wide range to signal processing, reproduction and amplification of sound and wireless communications. Without going in much detail, few efficient works accomplished by eminent
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Eur. Phys. J. Plus
(2020) 135:737
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