Geodesic
Determination of the inhomogeneity laws of a cylinder covering located in a plane waveguide for providing minimum sound reflection
Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 354-368

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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.
Keywords: diffraction, sound waves, elastic cylinder, non-uniform elastic coating, inhomogeneity laws, plane waveguide. 
@article{CHEB_2020_21_4_a29,
     author = {L. A. Tolokonnikov and A. E. Belkin},
     title = {Determination of the inhomogeneity laws of a cylinder covering located in a plane waveguide for providing minimum sound reflection},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {354--368},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_4_a29/}
}
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L. A. Tolokonnikov; A. E. Belkin. Determination of the inhomogeneity laws of a cylinder covering located in a plane waveguide for providing minimum sound reflection. Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 354-368. http://geodesic.mathdoc.fr/item/CHEB_2020_21_4_a29/