Scattering by a Cylinder with an Inhomogeneous Coating of Sound Waves, Emitted by a Linear Source in a Plane Waveguide

• Published in: Mathematical models and computer simulations 2022, Vol.14 (2), p.250-260
• Main Authors: Tolokonnikov, L. A., Larin, N. V.
• Format: Article
• Language: English
• Subjects: Acoustics; Boundaries; Cartesian coordinates; Circular cylinders; Continuous coating; Cylindrical bodies; Cylindrical waves; Helmholtz equations; Ideal fluids; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Modulus of elasticity; Plane waves; Protective coatings; Simulation and Modeling; Sound diffraction; Sound waves; Wave diffraction; Wave functions; Waveguides
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048222020156

The article is devoted to the mathematical modeling of an acoustic field scattered by an absolutely rigid circular cylinder with a continuously inhomogeneous elastic coating placed in a plane waveguide filled with an ideal fluid. The density and 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. The primary disturbance field is a harmonic sound wave emitted from a linear source. The acoustic field in the waveguide is sought as the sum of the contributions from the source and the scatterer. The contribution from the scatterer is determined by solving the problem of diffraction of a cylindrical sound wave by a rigid cylinder with a continuously inhomogeneous elastic coating in free space. Using the integral form of recording the cylindrical wave and the integral representation of the cylindrical wave functions in terms of Cartesian basic solutions of the Helmholtz equation, the contributions from the source and the scatterer are found in the form of a superposition of plane waves, taking into account multiple reflections from the waveguide boundaries. The results of calculations of the acoustic field in a waveguide are presented, when one boundary of the waveguide is absolutely rigid and the other slightly differs from the acoustically soft one. It is shown that with the help of an inhomogeneous coating it is possible to change the sound-reflecting properties of a cylindrical body in a waveguide.