Boundary integral equation method for the analysis of acoustic scattering from line-2 elastic targets (Q1961115)

For a transient acoustic wave, the authors consider the diffraction by an axisymmetric shell composed of a cylinder bounded by hemispherical endcaps (called here line-2). Its time-dependent response is expanded in terms of resonance modes of the fluid-loaded structure. The authors determine resonance frequencies as solutions of a nonlinear eigenvalue problem described by homogeneous equations governing the structure displacement coupled to acoustic radiated pressure. The resonance modes of the coupled system are the corresponding eigenvectors. Both hemisphere and cylinder equations are based on the Donnell-Mushtari approximation, which also governs thin shell oscillations. Modelling of the sound pressure by a hybrid potential-integral representation leads to a system of integro-differential equations defined on the surface of structure only (boundary integral equations). The unknowns, the hybrid potential density and the shell displacement vector, are expanded into Fourier series with respect to the natural cylindrical coordinate. Each angular component of the unknown functions is expanded into a series in Legendre polynomials, the coefficients of which are calculated by Galerkin method applied to the energetic form of equations.