Interaction of a plane progressive sound wave with anisotropic cylindrical shells

Abstract

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.