(5)Reflection of plane waves from a micropolar thermoelastic solid half-space with impedance boundary conditions

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Baljeet Singh ^a,∗, Anand Kumar Yadav ^b,  Deepak Gupta ^b

^a Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh, India 

^b Department of Mathematics, M.M. University Mullana, Ambala, India 

Received 5 December 2018; received in revised form 11 February 2019; accepted 12 February 2019 

Available online 26 February 2019 

Abstract  

    In this paper, the governing equations of linear, isotropic, homogeneous and generalized micropolar thermoelasticity are specialized in a plane. The governing equations are solved for plane harmonic wave solutions. Two separate velocity equations are obtained which indicate the existence of four plane waves with distinct speeds. A problem on reflection of plane waves from a thermally insulated/ isothermal surface is considered with impedance boundary conditions. Appropriate potentials for incident and reflected waves are formulated which satisfy the boundary conditions at a plane surface. Relations between reflection coefficients as well as the expressions of energy ratios for various reflected waves are obtained. For illustration, the reflection coefficients and energy ratios of reflected waves are computed for relevant material parameters of an aluminium-epoxy composite. Effect of impedance parameters on all reflected waves is shown graphically at each angle of incidence. 

© 2019 Shanghai Jiaotong University. Published by Elsevier B.V. 

This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)  

Keywords: Micropolar thermoelasticity; Impedance boundary; Plane waves; Reflection coefficients; Energy ratios.