The scattering of sound by two semi-infinite parallel staggered plates. II. Evaluation of the velocity potential for an incident plane wave and an incident duct mode

I. Abrahams, G. R. Wickham
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引用次数: 22

Abstract

In a recent paper Abrahams & Wickham showed how to exactly solve the diffraction problem for two parallel semi-infinite plates that are arranged to form a duct. The edges of the plates are misaligned so that the geometry is asymmetric with respect to the central line of the duct. In this paper we examine in detail the effect of this asymmetry on the field radiated from the duct when a fundamental travelling mode is excited within it, and the scattered field when a plane wave is excited at infinity. To evaluate the field in either case it is first necessary to solve the integral equations derived in our paper. Here we show how this is effected using the expansion theorem also enunciated in that paper. This solution is then used to calculate a number of physically interesting quantities such as the variation of the energy capture by the duct (when irradiated by an incident plane wave) as the stagger is increased and the asymmetric radiation pattern from an incident duct mode. The numerical computations are checked using an energy balance argument and, finally, a simple heuristic approximation is given for the scattering problem that in many situations accurately reproduces the essential physical characteristics of the solution.
两个半无限平行交错板对声音的散射。2对入射平面波和入射管道模式的速度势的评估
在最近的一篇论文中,亚伯拉罕和威克姆展示了如何精确地解决两个平行的半无限板排列成一个管道的衍射问题。板的边缘是不对齐的,因此几何形状是不对称的,相对于管道的中心线。在本文中,我们详细地研究了这种不对称性对管道内激发基本行模时辐射场的影响,以及在无限远处激发平面波时散射场的影响。要计算这两种情况下的场,首先需要解出本文导出的积分方程。在这里,我们用那篇论文中阐述的展开式定理来说明这是如何实现的。这个解决方案然后被用来计算一些物理上有趣的量,比如当错开增加时,管道捕获的能量(当被入射平面波照射时)的变化,以及来自入射管道模式的不对称辐射模式。最后,对散射问题给出了一个简单的启发式近似,该近似在许多情况下准确地再现了解的基本物理特性。
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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