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The reflection of plane waves in a micropolar fiber-reinforced thermoelastic medium under impedance boundary condition

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Abstract

This paper investigates the reflection of plane waves at the free surface of a micropolar fiber-reinforced medium using the three-phase lag thermoelasticity theory. An impedance type of boundary condition is being adapted at the free surface of the half-space. The harmonic mode analysis technique is applied to solve the coupled wave equations. Our investigation indicates the existence of a transverse wave and three coupled reflected waves at the free surface. The effects of rotation, stress, and micropolarity on the attenuation coefficient, phase velocity, and reflection ratio of all four reflected waves have been examined numerically using MATLAB. This paper is notable for observing some interesting phenomena, such as critical angles and critical frequencies for attenuation coefficients and reflection ratios, respectively. Also, some interesting results have been obtained by comparing our results to those obtained using the GN-III theory of thermoelasticity. Moreover, the paper provides an explicit form of energy ratios and depicts them graphically. It also justifies that the summation of energy ratio is unity in the selected range of angle of incidence.

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Acknowledgements

The authors sincerely thanks Applied Mathematics and Geomechanics (AMG) Lab, Department of Mathematics, IIT Indore for providing the research facilities. One of the authors, Dr. Santanu Manna, also thanks the SERB, Government of India for financial support under project number MTR/2022/000114.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Indore, Indore, Madhya Pradesh, 453552, India

    Santanu Manna, Adarsh Jain & Dipendu Pramanik

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  1. Santanu Manna
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  2. Adarsh Jain
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Correspondence to Santanu Manna.

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Manna, S., Jain, A. & Pramanik, D. The reflection of plane waves in a micropolar fiber-reinforced thermoelastic medium under impedance boundary condition. Eur. Phys. J. Plus 138, 967 (2023). https://doi.org/10.1140/epjp/s13360-023-04551-8

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