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Interaction of a plane progressive sound wave with anisotropic cylindrical shells

机译：平面渐进声波与各向异性圆柱壳的相互作用

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摘要

An exact analysis based on the wave function expansion is carried out to study the scattering of a plane harmonic acoustic wave incident at an arbitrary angle upon an arbitrarily thick helically filament-wound (anisotropic) cylindrical shell submerged in and filled with compressible ideal fluids. Using the laminated approximation method, a modal state equation with variable coefficients is set up in terms of appropriate displacement and stress functions and their cylindrical harmonics to present an analytical solution based on the three-dimensional exact equations of anisotropic elasticity. Taylor's expansion theorem is then employed to obtain the solution to the modal state equation, ultimately leading to calculation of a transfer matrix. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the background (non-resonance) and resonance components from it. The solution is particularly used for the isolation and identification of excited resonances of an air-filled and water submerged Graphite/ Epoxy cylindrical shell as the circumnavigating helically propagating waves. In addition, the sensitivity of resonances associated with various modes of wave propagation appearing in the backscattered amplitude to the perturbation in the material's elastic constants is examined. Furthermore, non-axisymmetric dynamic behavior of the anisotropic shell is illustrated by analyzing the directivity pattern associated to the angular distribution of the far-field form function amplitude. The effects of winding angle of filaments and the shell wall-thickness on the frequency response of the shell are also investigated. For verification, the wave propagation characteristics of the anisotropic shell (which have been extracted from the main body of the solution) and the far-field form function amplitude of a limiting case are considered and fair agreement with the solutions available in the literature are established.
机译：进行了基于波函数展开的精确分析，研究了以任意角度入射在浸没并充满可压缩理想流体的任意厚度的螺旋状细丝缠绕（各向异性）圆柱壳上的平面谐波声波的散射。使用分层近似法，根据适当的位移和应力函数及其圆柱谐波，建立了具有可变系数的模态状态方程，以基于各向异性弹性的三维精确方程，给出了一种解析解。然后使用泰勒展开定理获得模态方程的解，最终导致传递矩阵的计算。遵循经典的声共振散射理论（RST），通过构造分波并从中获得背景（非共振）和共振分量来确定散射场和对表面波的响应。该解决方案特别用于隔离和识别充气和水浸石墨/环氧树脂圆柱壳作为绕行螺旋传播波的激发共振。另外，检查了与以反向散射振幅出现的各种波传播模式相关的共振对材料弹性常数的扰动的敏感性。此外，通过分析与远场形式函数振幅的角度分布相关的方向性图来说明各向异性壳的非轴对称动力学行为。还研究了细丝的缠绕角度和壳壁厚度对壳的频率响应的影响。为了验证，考虑了各向异性壳的波传播特性（已从解决方案的主体中提取）和极限情况的远场形式函数幅度，并与文献中的解决方案建立了合理的一致性。 。

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