SUMMARY
Bich Nataliya Nikolajevna
Sounds fields modeling in multilayered areas
Keywords: Helmholtz equation, method of separation of variables, the scattering of sound waves, spherical coordinates, Bessel functions, Hankel functions, Legendre functions, dual series equations, Legendre polynomials.
The aim of the thesis: mathematical modeling of scattering sound fields on screens system, including the thin unclosed shell; development of research methods based on patterns, constructed in the thesis; software implementation of the developed in the thesis research methods in the computer algebra system MathCad for obtaining quantitative characteristics, reflecting the results of research methods.
Research methods: in this work, for solving problems of scattering of the sound field on the system screens the method of separation of variables, analytical methods based on addition theorems for the wave functions of the summary equations was used.
The obtained results and their novelty. Built analytical model of the scattering of the sound field on the system screens: unclosed spherical shell is elongated (flattened) ellipsoid of revolution; unclosed spherical shell - multi-layer body (plane, cylinder, sphere); unclosed spherical shell - elastic body (plane, cylinder, sphere). For the first time the spherical radiator was considered as the field source inside a thin unclosed spherical shell what is important for the development of shielding structures. Software for numerical analysis of the display characteristics of the considered problems was developed.
Extent of use and area of application. The results have wide application for the solution of diffraction problems of acoustics in physics, in information and measurement technology, industry, medicine, biology, military Affairs. The Developed simulation methods can be used to test the characteristics of sound fields in multiply connected areas. The Developed algorithms and software systems have found their implementation in educational process. Results of the solution of a problem of shielding on screens: the permeable flat cover is multilayered, an elastic flat cover are introduced in the manufacture.