(4)Reflection and transmission of elastic waves at an interface between two micropolar piezoelectric half-spaces

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Baljeet Singh ^a,∗, Asha Sangwan ^b,  Jagdish Singh ^c

^a  Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh 160011, India 

^b Department of Mathematics, Government College, Sampla, Rohtak 124001, Haryana, India 

^c Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, Haryana, India 

Received 1 March 2019; received in revised form 21 April 2019; accepted 21 April 2019 

Available online 25 April 2019 

Abstract 

    In the present paper, we consider a problem of reflection and transmission of plane waves at an interface between two different transversely isotropic micropolar piezoelectric half-spaces. The plane wave solution of governing equations for micropolar piezoelectric medium indicates the propagation of three coupled plane waves. An incident plane wave at an interface between two dissimilar half-spaces generates three reflected and three transmitted waves. The relations between amplitude ratios of reflected and transmitted waves are derived which, in general, depend on material parameters and angle of incidence. The explicit expressions for energy ratios of reflected and transmitted waves are also obtained. For relevant material parameters, the results are illustrated graphically to show the micropolar piezoelectric effects on variations of amplitude ratios and the square root of energy ratios against the 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: Plane waves; Micropolar piezoelectricity; Reflection and transmission; Amplitude ratios; Energy ratios.