Scattering by a cylinder with an inhomogeneous coating of sound waves emitted by a linear source in a plane waveguide

The article is dedicated to the mathematical modeling of the acoustic field, which is scattered by the absolutely rigid circular cylinder with the continuously inhomogeneous coating. The cylinder is placed in a flat waveguide, which is filled with an ideal fluid. Density and the elastic moduli of the coating material are described by continuous functions of the radial coordinate. One of the waveguide boundaries is ideal (absolutely hard or acoustically soft), while the other differs arbitrarily little from the ideal one. The primary perturbation field is a harmonic sound wave emitted by a long linear source. The acoustic field in the waveguide is investigated as the sum of the source and the scatterer contributions. The scatterer contribution is determined on the basis of the problem solution of the cylindrical sound wave diffraction by the rigid cylinder with the continuously inhomogeneous elastic coating located in free space. Using the integral form of the cylindrical wave recording and the integral representation of wave cylindrical functions by the Cartesian basis solutions of the Helmholtz equation, the contributions from the source and the scatterer are in the form of a superposition of plane waves in terms of the multiple reflections from the waveguide boundaries. The results of calculations of acoustic fields in a waveguide are presented, when one boundary of the waveguide is absolutely rigid and the other slightly differs from acoustically soft. We showed that with the help of the inhomogeneous coating it is possible to change the sound reflecting properties of a cylindrical body in a waveguide.