Open AccessMathematical modeling of monochromatic acoustic wave diffraction on a system of bodies and on flat screens
Author(s) -
С.Г. Даева,
A L Beskin,
N N Trokhachenkova
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2142/1/012002
Subject(s) - diffraction , monochromatic color , piecewise , acoustic wave equation , field (mathematics) , wave equation , acoustic wave , integral equation , mathematical analysis , mathematics , boundary value problem , point (geometry) , geometrical acoustics , acoustics , physics , optics , geometry , pure mathematics
Some problems of diffraction of a monochromatic acoustic wave on surfaces of complex shapes are considered. To solve such problems, an approach is applied, in which the problem is reduced to a boundary hypersingular integral equation, where the integral is understood in the sense of a finite value according to Hadamard. Such approach allows solving diffraction problems both on solid objects and on thin screens. To solve the integral equation, the method of piecewise constant approximations and collocations, developed in the previous works of the author, is used. In the present study, examples of modeling the diffraction of an acoustic wave by bodies with partial filling are given. It is shown how the filling of bodies influences the acoustic pressure field, and the field direction patterns are given. An example of applying this approach to solving the problem of sound propagation in an urban area is also given: the diffraction of an acoustic wave from a point source on a system of buildings is considered. The presented results demonstrate that this method allows constructing reflected fields and analyze their characteristics on surfaces of complex shapes.