平面声波斜入射到水中无限圆柱的纯弹性共振散射

Pure Elastic Resonance Scattering of an Obliquely Incident Plane Acoustic Wave by a Submerged Infinite Cylinder

水下弹性柱的声散射问题已得到广泛而深入的研究，但仅有很少的文章讨论斜入射情形。本文导出了平面声波斜入射时水中无限圆柱纯弹性共振散射函数的简单而明显的表达式。并针对实心铝柱详细计算了不同入射角时纯弹性共振散射的分波共振谱，还同时给出了远场反向散射形态函数及其刚硬背景隔离，特别对几个临界角附近的共振特性进行了分析、对于斜入射时所特有的区别于原有共振模式的附加共振，本文详细讨论了其产生机制和特有性质。文中详细计算了斜人射时无因次复频率平面上的共振复极点分布，并由此计算了不同入射角时各阶共振模式，特别是附加共振模式所对应螺旋环绕波的相速度频散曲线。

Although sound scattering by submerged elastic cylinders has been extensively studied, only a few works aimed at the case of obliquely incidence. In this paper, we derive a simple and explicit expression of the pure elastic resonance scattering function of a submerged infinite cylinder excited by a plane wave at obliquely incidence. For backscattering of a solid aluminum cylinder we have calculated (a) the partial resonance spectra n=0-7, (b) the far field total form functions and the pure elastic resonance form functions,(c) the complex resonance poles in the normalized complex frequency plane, and (d) the dispersion curves of the first several families of belieal waves, at various incident angles in details. We especially discuss the generation mechanism and properties of the complementary resonatlce modes existing only at obliquely incidence. Our attentions are also focused on the variance of the resonance spectra with the incident angle,particularly near several critical angles.