The mathematical model of reflection and refraction of longitudinal waves in thermo-piezoelectric materials

In this paper, the basic equations of motion, of Gauss and of heat conduction, together with constitutive relations for pyro- and piezoelectric media, are presented. Three thermoelastic theories are considered: classical dynamical coupled theory, the Lord–Shulman theory with one relaxation time and Green and Lindsay theory with two relaxation times. For incident elastic longitudinal, potential electric and thermal waves, referred to as qP, φ-mode and T-mode waves, which impinge upon the interface between two different transversal isotropic media, reflection and refraction coefficients are obtained by solving a set of linear algebraic equations. A case study is investigated: a system formed by two semi-infinite, hexagonal symmetric, pyroelectric–piezoelectric media, namely Cadmium Selenide (CdSe) and Barium Titanate (BaTiO₃). Numerical results for the reflection and refraction coefficients are obtained, and their behavior versus the incidence angle is analyzed. The interaction with the interface give rises to different kinds of reflected and refracted waves: (i) two reflected elastic waves in the first medium, one longitudinal (qP-wave) and the other transversal (qSV-wave), and a similar situation for the refracted waves in the second medium; (ii) two reflected potential electric waves and a similar situation for the refracted waves; (iii) two reflected thermal waves and a similar situation for the refracted waves. The amplitudes of the reflected and refracted waves are functions of the incident angle, of the thermal relaxation times and of the media elastic, electric, thermal constants. This study is relevant to signal processing, sound systems, wireless communications, surface acoustic wave devices and military defense equipment.