A Short Survey on Green’s Function for Acoustic Problems

IF 1.3 3区 物理与天体物理 Q3 ACOUSTICS
Augustus R. Okoyenta, Haijun Wu, Xueliang Liu, Weikang Jiang
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引用次数: 5

Abstract

Green’s functions for acoustic problems is the fundamental solution to the inhomogeneous Helmholtz equation for a point source, which satisfies specific boundary conditions. It is very significant for the integral equation and also serves as the impulse response of an acoustic wave equation. They are important for acoustic problems that involve the propagation of sound from the source point to the observer position. Once the Green’s function, which satisfies the necessary boundary conditions, is obtained, the sound pressure at any point away from the source can be easily calculated by the integral equation. The major problem faced by researchers is in the process of constructing these Green’s functions which satisfy a specific boundary condition. The aim of this work is to review some of these fundamental solutions available in the literature for different boundary conditions for the ease of analyzing acoustics problems. The review covers the free-space Green’s functions for stationary source and rotational source, for both when the observer and the acoustic medium are at rest and when the medium is in uniform flow. The half-space Green’s functions are also summarized for both stationary acoustic source and moving acoustic source, derived using the image source method, equivalent source method and complex equivalent method in both time domain and frequency domain. Each of these methods used depends on the different impedance boundary conditions for which the Green’s function will satisfy. Finally, enclosed spaced Green’s functions for both rectangular duct and cylindrical duct for an infinite and finite duct is also covered in the review.
浅谈格林函数在声学问题中的应用
声学问题的格林函数是点源非齐次亥姆霍兹方程的基本解,它满足特定的边界条件。它对积分方程有重要意义,也可作为声波方程的脉冲响应。它们对于涉及声音从源点传播到观测者位置的声学问题是重要的。一旦得到满足必要边界条件的格林函数,就可以用积分方程很容易地计算出远离声源的任何一点的声压。研究人员面临的主要问题是如何构造满足特定边界条件的格林函数。本工作的目的是回顾文献中针对不同边界条件的一些基本解决方案,以便于分析声学问题。本文综述了在观察者和声介质处于静止状态和介质处于均匀流动状态时,固定声源和旋转声源的自由空间格林函数。总结了静止声源和运动声源的半空间格林函数,分别在时域和频域分别用像源法、等效源法和复等效法推导了半空间格林函数。这些方法中的每一种都取决于格林函数所满足的不同阻抗边界条件。最后,本文还讨论了矩形风管和圆柱风管对于无限和有限风管的封闭间隔格林函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Theoretical and Computational Acoustics
Journal of Theoretical and Computational Acoustics Computer Science-Computer Science Applications
CiteScore
2.90
自引率
42.10%
发文量
26
期刊介绍: The aim of this journal is to provide an international forum for the dissemination of the state-of-the-art information in the field of Computational Acoustics. Topics covered by this journal include research and tutorial contributions in OCEAN ACOUSTICS (a subject of active research in relation with sonar detection and the design of noiseless ships), SEISMO-ACOUSTICS (of concern to earthquake science and engineering, and also to those doing underground prospection like searching for petroleum), AEROACOUSTICS (which includes the analysis of noise created by aircraft), COMPUTATIONAL METHODS, and SUPERCOMPUTING. In addition to the traditional issues and problems in computational methods, the journal also considers theoretical research acoustics papers which lead to large-scale scientific computations.
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