Liouville–Green approximation for Bleustein–Gulyaev waves in functionally graded materials

The present work aims at studying Bleustein–Gulyaev (BG) waves in a specific class of functionally graded materials. The inhomogeneity under question requires that the elastic stiffness, the piezoelectric term and the dielectric term all vary proportionally to the same inhomogeneity function. However, the density is allowed here to vary in a different manner. As a result we are able to analyse BG waves for media with variable bulk Shear Horizontal (SH) wave velocity profiles. We make use of the Liouville–Green approximation for second order Matrix Differential Equations, with explicit computable error bounds. Our analysis is limited to a certain integrability condition and to the numerical evaluation of a series of improper integrals. We present dispersion curves for BG waves for the metalized boundary condition for different inhomogeneity profiles. The results show that variations in the SH bulk wave velocities have a profound effect on the BG dispersion curves for the metalized boundary condition.