Abstract

Several anomalies of wave scattering that occur in acoustic waveguides with cylindrical or corrugated rigid walls at frequencies close to the cut-off points (thresholds) of continuous spectrum are considered. The notion of threshold resonances generated by “almost standing waves”, which cause no energy transfer to infinity, is introduced. For corrugated waveguides, examples are presented to illustrate the opening of spectral gaps (wave stopping zones) and eigenvalues near their edges and common or degenerate thresholds. Weinstein’s and Wood’s anomalies are described, which occur above and below the thresholds and manifest themselves in “almost complete” reflection and transmission of waves, and in disproportionally fast variation of the diffraction pattern, respectively. Examples of complete wave transmission (“invisibility of obstacle”) are discussed along with the procedures of sharpening and smoothing of Wood’s anomalies, specifically, formation of eigenvalues embedded into the continuous spectrum and corresponding trapped waves. The Sommerfeld, Umov–Mandelshtam, and limiting absorption principles are compared along with the specific features of their application at thresholds.

中文翻译：

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连续谱截止点附近的声波散射异常（综述）

摘要

考虑了在具有圆柱形或波纹状刚性壁的声波导管中，以接近连续频谱的截止点（阈值）的频率发生的几种波散射异常。引入了由“几乎驻波”产生的阈值共振的概念，该共振不会引起能量转移到无穷大。对于波纹波导，给出了一些示例来说明频谱间隙（波阻区）和其边缘附近的特征值以及共同或简并阈值的打开。描述了Weinstein和Wood的异常，这些异常发生在阈值之上和之下，并分别以“几乎完全”的波反射和透射以及衍射图的不成比例的快速变化表现出来。讨论了完整波传输的示例（“障碍物的隐身性”），以及对Wood异常进行锐化和平滑的过程，尤其是嵌入到连续光谱中的特征值的形成以及相应的陷波。比较了Sommerfeld，Umov–Mandelshtam和极限吸收原理，以及它们在阈值下的应用特点。