Boundary Integral Equations Method for the Analysis of Acoustic Scattering from Line-2 Elastic Targets

Abstract

The prediction of the acoustic scattering from elastic structures is a recurrent problem of practical importance as, for example, in underwater detection and target identification. We aim at setting out the diffraction problem of a transient acoustic wave by an axisymmetric shell composed of a cylinder bounded by hemispherical endcaps, called Line-2. Its time-dependent response is expanded in terms of the resonance modes of the fluid-loaded structure. The latter are well suited when the structure is submerged in a heavy fluid: it is an alternative to modal methods whose expansions as series of natural modes of the in vacuo shell are much better for describing the interaction between a structure and a light fluid. The resonance frequencies are defined as solutions of the nonlinear eigenvalue problem described by the set of homogeneous equations governing the structure displacement coupled to the acoustic radiated pressure. The resonance modes of the coupled system are the corresponding eigenvectors.

Both hemisphere and cylinder equations are modeled by the approximation of Donnel and Mushtari which governs thin shells oscillations. The modeling of the sound pressure by a hybrid potential integral representation leads to a system of integro-differential equations defined on the surface of the structure only (boundary integral equations). The unknowns, the hybrid potential density as well as the shell displacement vector, are developed into Fourier series with respect to the natural cylindrical coordinate. Each angular component of the unknown functions is then expanded as series of Legendre polynomials, the coefficients of which are calculated thanks to a Galerkin method derived from the energetic form of the equations.

The whole method can also be applied to predict the response of the coupled structure to a harmonic or a random excitation.