Application of the boundary element method to coupled fluid-structure interaction problems

Abstract

<p>The direct boundary element method (BEM) is used to formulate and numerically simulate the interaction of acoustic waves with submerged elastic structures and subsequently specialized to model finite beam transmission through locally curved elastic surfaces. These are structural-acoustic or fluid-solid interaction problems coupling scalar (acoustic) and vector (elastic) media. The problem is formulated in the frequency domain and modelled in three dimensions, and the elasto-acoustic phenomenon described by the acoustic and elastodynamic boundary integral equations (BIE) with pressure and displacement serving as the primarily variables;The general problem deals with a closed solid domain surrounded by an unbounded fluid medium so that with the well known radiation condition, the integral formulation requires modelling only the fluid-solid interface. This formulation is valid for both the exterior scattering/radiation behavior and the field transmitted into the elastic domain. A FORTRAN program (FS3D) was developed and implements the BEM approach using point collocation and isoparametric quadratic shape functions and provides pressure and displacements on the surface of the structure. The code includes separate acoustic and elastic post-processors to generate the far-field fluid pressure and the transmitted interior elastic displacements. Incident wave or the acoustic source is arbitrary but is normally taken to be either a plane or spherical wave or a bounded beam of any given form. The accuracy of the BEM approach is tested for simple shapes like spheres, spheroids and cylinders. Examples illustrate the structural response and acoustic field due to solids of different elastic properties and fluids of different impedances;The capability developed for the general problem is extended to a specific application, namely the reflection and transmission of an ultrasonic beam through an open interface. Wave mechanics of this type is an important part of nondestructive ultrasonic immersion testing where the interface is the surface of the component being probed. That surface, if locally flat, can be modelled as a flat half-space or it might have local curvature. Infinite domains, under certain assumptions, are readily approximated with an easy modification of the BEM formulation. The formalism is verified by an exact analysis of a Gaussian beam transmitted through a flat interface and by studying the ability of the solutions to satisfy the elastodynamic reciprocity relations for concave and convex interfaces;Various features of the coupling phenomenon and the BIE formalism are discussed, including instability of the coupled matrix at special eigenfrequencies (fictitious eigenfrequencies). The accuracy to be expected in a scattering problem at or near these frequencies is investigated and illustrated for the case of an elastic sphere in a fluid. Surface wave phenomenon encountered during non-normal incidence on an interface is also analyzed and various aspects of their modelling discussed.</p>