Perturbation of Bleustein–Gulyaev Waves in Piezoelectric Media: Barnett and Lothe Integral Formalism Revisited

This paper studies surface waves called Bleustein–Gulyaev (BG) waves in piezoelectricity. They propagate along the surface of a homogeneous piezoelectric half-space whose constituent material has C6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C_{6}$\end{document} hexagonal symmetry, where the surface is subject to the mechanically-free and electrically-closed condition. We revisit the Barnett–Lothe integral formalism for general piezoelectricity and give straightforward proofs, which only use the positive definiteness of the elasticity tensor and of the dielectric tensor, to derive fundamental properties of the Barnett–Lothe tensors. This leads us to obtain a criterion for the existence of subsonic surface waves. Moreover, when the waves propagate in the direction of the 1-axis along the surface of the piezoelectric half-space x2≤0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x_{2}\le0$\end{document} of C6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C_{6}$\end{document} hexagonal symmetry whose 6-fold axis of rotational symmetry coincides with the 3-axis, we compute explicitly the phase velocity of the BG waves and investigate its perturbation, i.e., the shift in the velocity due to a perturbation of the material constants which need not have any symmetry.