Abstract

We study the propagation of waves in a waveguide which is the union of two semi-infinite cylinders connected by a thin rectangular ligament. It is shown that almost complete or even complete transmission of the piston mode at a prescribed frequency can be achieved via fine tuning of the plate sizes, although, of course, almost complete wave reflection occurs in the generic case. The result is obtained by applying an asymptotic analysis of the scattering coefficients of the acoustic wave, in particular, by using the dimension reduction procedure on the thin ligament. Possible generalizations of the problem formulation and related open questions are discussed.

中文翻译：

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由扁平韧带连接的两个半无限圆柱中声波传播的异常

摘要

我们研究波在波导中的传播，波导是由细矩形韧带连接的两个半无限圆柱体的联合。结果表明，通过微调板尺寸可以实现在指定频率下几乎完全或什至完全传输活塞模式，当然，在一般情况下会发生几乎完全的波反射。结果是通过应用声波散射系数的渐近分析获得的，特别是通过对薄韧带使用降维程序。讨论了问题表述和相关开放问题的可能概括。