Transference of shear horizontal waves in a functionally graded piezoelectric structure

Abstract

A brief analysis of the transference of shear horizontal wave has been carried out in a functionally graded half-spaces bonded imperfectly. The top half-space is functionally graded piezoelectric material whereas the bottom half-space is elastic substrate and top half-space is graded quadratically. To obtain the solution in upper half-space, the partial differential equation is transformed into an ordinary differential equation using the variable-separable method, and WKB asymptotic technique is employed to derive analytic solutions for the functionally graded half-space, enabling the determination of dispersion relations in the form of a determinant. Reflection and transmission coefficients, representing ratios of wave amplitudes, are derived for an imperfect boundary. Numerical analysis focuses on a specific model and the graphical interpretation of results is facilitated using Mathematica-7.

Keywords

• Transverse wave
• Functionally graded material
• Gradedness parameter
• Wentzel–Kramers–Brillouin asymptotic approach
• Reflection and transmission coefficients