Rational Two Dimensional Analysis of Reflecting SH Waves from an Gradient Inhomogeneous Layer.

Abstract

Introducing a rationalized layer element for a two-dimensional elastic analysis of a gradient inhomogeneous material, the reflectance is successfully estimated without any complexities. In the reflection and transmission analysis of elastic waves impinging on a gradient inhomogeneous layer, the difficulty comes out in the evaluation of modified Bessel functions of imaginary order depending on the inhomogeneous parameter. Then the main subject is discussion of a strategic tackle to overcome the difficulty. Rational analysis presented here is the use of a rationalized inhomogeneous layer element in stead of the previously developed element so called LILE. Development of the rationalized new elements and their availability have been explained. As the results, the method by using the new element is very convenient to the analysis of gradient inhomogeneous materials, because the fundamental solutions in the rational analysis are expressed by elementary functions, and the reflectance calculation can be carried out without any use of the modified Bessel functions for any inhomogeneous parameters, as far as it concerns in this study. The trial numerical results by using only one new element, coincide well with the exact numerical results obtained by multistacking layer model of many homogeneous elements.