A comparison between the boundary element method and the wave superposition approach for the analysis of the scattered fields from rigid bodies and elastic shells

Abstract

The steady state analysis of the scattering of plane acoustic waves from submerged rigid and elastic bodies using two approaches is presented. The first approach uses a combined finite element/boundary element (FE/BE) methodology. The NASA structural analysis (NASTRAN) program is used to formulate the structural matrices based on the finite element method (FEM). The surface integral equation radiation and scattering (SIERRAS) program creates the fluid matrices based on the boundary element method (BEM) and solves the coupled fluid-structure interaction problem. A superparametric boundary element (BE) with nine nodes is employed. The combined Helmholtz integral equation formulation (CHIEF) is employed to provide a unique solution for all frequencies. In the second approach, the superposition method (SUP) is used for modeling the fluid. The SUP method is an off-boundary approach that employs a number of point sources moved inside the body to represent the fluid response at the surface. This allows the fluid matrices to be formed without surface integration. Formulations for the SUP method are introduced for both the radiation and scattering problems. The program SUPER reads the NASTRAN structural matrices and solves the combined FE/SUP fluid-structure equations. The FE/BEM and FE/SUP methods are applied to the scattering of an infinite set of plane waves from a submerged rigid sphere, rigid prolate spheroid, right cylinder, and from an elastic cylindrical shell with hemispherical endcaps. The SUP method is found to be easier to implement and to provide an accurate result at internal resonance frequencies where the BEM requires additional equations to ensure an accurate solution.

Review: The Use of Equivalent Source Method in Computational Acoustics

“…Koopmann et al 47 and Miller et al 48 presented that the WSM avoids nonuniqueness at critical interior resonance frequencies that occur in the BEM, as discussed earlier. However, the resolution of the nonuniqueness problem in the WSM was questioned by other researchers.…”

“…Earlier work addressed that the ESM is more accurate and more efficient than the BEM. Miller et al 48 compared the ESM (or WSM) with the BEM for acoustic scattering for rigid bodies or elastic shell structures. Figure 2 shows a comparison between the BEM and the WSM for the scattering by a cylindrical shell.…”

Subcritical scattering from buried elastic shells

“…For example, Kessel 25 used a similar internal multipole expansion method in combination with a modal Green's function to model the scattering from objects in horizontally stratified waveguides, but again using ideal, homogeneous boundary conditions. Also, Kessel's, like Miller's, 26 approach does not allow the target to penetrate the waveguide interfaces and does not incorporate multiple scattering between the target and the adjacent boundaries. In addition, Sarkissian 27 did use a virtual source model to describe scattering by discrete objects in a waveguide, but the objects were not elastic and they were not buried in the sediment, therefore simplifying the theoretical approach, eliminating the structural and a number of environmental effects.…”

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions

“…The main deficiency of the wave superposition methods ͑also the off-boundary methods͒ lies in the selection of the inner surface, particularly when the boundary surface has discontinuities. Miller et al 29 proposed some rules for selecting the inner surface; however, the optimum inner surface was determined by a process of trial and error. Krutitskii 30 developed a modified formulation that combined Kupradze's simple source method 24 and the principle of wave superposition without numerical implementation; that is, monopoles were distributed on the radiation/scattering body and inner surfaces.…”