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Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

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Petroleum Science 2019年第2期16卷 298-317页

作者： M.Kumar M.S.Barak M.Kumari Department of Mathematics B R Ambedkar Govt. College Department of Mathematics Indira Gandhi University

Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves(i.e., incident and reflected) in an elastic medium are considered as homogeneous(i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous(i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity *** has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.

关键词： Plane harmonic wave Double-porosity dual-permeability Reflection/refraction coefficients Energy share Elastic solid

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