About solutions of inverse problems sound waves diffraction

N. N. Dobrovol'skii ; N. V. Larin ; S. A. Skobel'tsyn ; L. A. Tolokonnikov

Čebyševskij sbornik, Tome 20 (2019) no. 3, pp. 220-245

Résumé

A review of works on solving the inverse problems of scattering of sound waves by elastic bodies is presented.The theoretical foundations for solving inverse problems of sound diffraction are based on fundamental studies of the problem of inverse problems for partial differential equations performed by Russian scientists.In the most general classification, inverse acoustic problems are divided into inverse radiation problems (IRP) and inverse scattering problems (ISP).When solving problems of the first class, the parameters of the sound field determine some parameters of the source.When solving the problems of the second class, the parameters of the scattered sound field are used to identify the properties of the scattering object.Most applications of acoustic methods are based on solving inverse diffraction problems when the parameters of an object or medium are judged by the parameters of the emitted or reflected sound field.Analysis of sound fields forms the basis of methods in hydro- and aeroacoustics;researches in biology and medicine;non-destructive testing and diagnostics of objects;ultrasonic flaw detection;inspection and testing of materials, structures and structures.The solutions of all inverse problems are based on the solution of direct diffraction problems.The paper presents the most significant results in solving direct problems of scattering of sound waves by elastic objects.The works devoted to the problems of inverse problems of sound scattering by inhomogeneous elastic bodies are singled out.This direction is the subject of interest in the research of the authors.

Détail

Keywords: sound waves diffraction, direct diffraction problem, inverse scattering problem, sound scattering by elastic bodies.