Determination of the inhomogeneity laws of a cylinder covering located in a plane waveguide for providing minimum sound reflection

Abstract

The article considers the inverse problem on determination of the inhomogeneity laws of an
elastic coating of an absolutely rigid cylinder located in a plane waveguide, one boundary of
which is absolutely hard and the other is acoustically soft.
It is believed that the waveguide filled by ideal fluid. The harmonic sound pressure wave
excited by a given distribution sources on the section of the waveguide located on the final
distance from the axis of the cylinder is propagated along the walls of the waveguide on normal
to the surface of the cylindrical body. The inhomogeneity parameters for providing minimum
sound reflection are determined.
The solution of the inverse problem is obtained based on the solution of the direct problem
diffraction.
Dependences of the density and elastic moduli of the coating material from the radial
coordinate are approximated by polynomials of the third degrees.
Functionals defined on the class of cubic functions and expressing the average intensity of
sound scattering in a given section of the waveguide at a fixed frequency or at some frequency
range are built.
The minimization of the functionals is done with using the genetic algorithm. Analytical
description of the optimal inhomogeneity laws of an cylinder coating are received to ensure
minimal sound reflection.