Mathematics

Elastic wave diffraction on a layer with fractal density distribution

A. V. Anufrieva^a, K. B. Igudesman^b, D. N. Tumakov<sup>a

a</sup> Institute of Computer Science and Information Technology, Kazan Federal University, Kazan
^b Institute of Mathematics and Mechanics, Kazan Federal University, Kazan

Abstract: The authors consider the diffraction of elastic wave on a layer with the fractal density. The problem is reduced to a system of ordinary differential equations with linear coefficients and its analytical decision is found. The researchers numerically investigate a layer with a fractal density, find peaks of energy of the reflected wave and illustrate dependence of reflected energy from self-similar properties of the fractal density.

Keywords: diffraction, elastic wave, fractal interpolation.

UDC: 519.6, 534.26