Study of the positional cross-section of acoustic wave scattering for a system of sound-permeable spheres
Views: 46 / PDF downloads: 58
DOI:
https://doi.org/10.32523/bulmathenu.2024/3.4Keywords:
system of sound-permeable spheres; scattered wave intensity; positional scattering cross-section; plane wave; monopole radiation sourceAbstract
In the frame of solving the acoustic scattering problem on a system consisting of many sound-permeable spheres, one of the main characteristics of the scattering phenomenon, namely, the positional scattering cross-section, is investigated. This characteristic allows one to analyze the intensity of a scattered wave in a fixed direction. The formula for this characteristic is transformed in the case of many scatterers, taking into account the interaction between the spheres in the system. This formula is applicable to any number of spheres in the system and their arbitrary distribution in 3D space. Two types of external pressure are considered --- a plane wave and a spherical wave from a monopole radiation source. The numerical algorithm is verified with the data of other numerical studies; qualitative agreement between the results is obtained. Numerical parametric analysis for a system consisting of two sound-permeable spheres showed that in the case when the density of the medium inside the spheres is much less than the surrounding medium, the system has the best scattering properties; backscattering in a system with spheres of the same radius is higher than in a system with spherical particles of different sizes; for a plane wave, an increase in the wave radius leads to a decrease in the value of the backscattering cross-section function, while for a monopole radiation source, an increase in the wave radius leads to an increase in this value. For a system containing a 121~drop of water in air, it was found that an increase in the distance between the centers of the spheres leads to an increase in the scattering properties of this layer in the opposite direction.
References
Martin~P.A. Acoustic scattering by one bubble before 1950: Spitzer, Willis, and Division 6~// J. Acoust. Soc. Am. -- 2019. -- Vol.~146. -- P.~ 920--926. DOI:~10.1121/1.5120127.
Насибуллаева~Э.Ш. Рассеяние звуковых волн на сферах: методы решения и основные характеристики (обзор)~// Многофазные системы. -- 2021. -- Т.~16, №~3--4. -- С.~88--104. DOI:~10.21662/mfs2021.3.013.
Насибуллаева~Э.Ш. Численный анализ многократного рассеяния акустической волны на множестве звукопроницаемых сфер в трехмерном пространстве~// Вычислительная механика сплошных сред. 2022. -- Т.~15, №~4. -- С.~383--398. DOI: 10.7242/1999-6691/2022.15.4.29.
Насибуллаева~Э.Ш. Моделирование акустического рассеяния от множества звукопроницаемых сфер в трехмерном пространстве~// Вычислительные технологии. -- 2022. Т.~27, №~2. -- С.~19--36. DOI: 10.25743/ICT.2022.27.2.003.
Насибуллаева~Э.Ш. Численный анализ акустического рассеяния от звукопроницаемых сфер при внешнем воздействии~// Вестник УГАТУ. -- 2021. -- Т.~25, №~2(92). -- С.~93--101. DOI: 10.54708/19926502_2021_2529293.
Гринченко~В.Т., Вовк~И.В., Мацыпура~В.Т. Основы акустики. Киев:~Наукова думка, 2009. -- 867~с.
Владимиров~В.С. Уравнения математической физики. Москва:~Наука, 1981. -- 512~с.
Корн~Г., Корн~Т. Справочник по математике для научных работников и инженеров. Москва:~Наука, 1974. -- 832~c.
Skaropoulos~N.C., Yagridou~H.D., Chrissoulidis~D.P. Interactive resonant scattering by a cluster of air bubbles in water~// J. Acoust. Soc. Am. -- 2003. -- V.~113, No.~6. -- P.~3001--3011. DOI: 10.1121/1.1572141.
Иванов~Е.А. Дифракция электромагнитных волн на двух телах. Минск:~Наука и техника, 1968. -- 584~с.
LAPACK~--- Linear Algebra PACKage. URL: https://netlib.sandia.gov/lapack/ (дата обращения: 12.09.2024).
Downloads
Published
How to Cite
Issue
Section
