A symmetrical formulation of coupled BEM/FEM for submerged structures based on acoustical reciprocity

Abstract

The paper presents a structural acoustics formulation for elastic structures submerged in water. The structural equation is described by a finite element method where the linear displacement variables on the wetted surface are chosen locally as one normal displacement and the other two displacements tangent to the wetted surface, whereas the rest of rotational displacements or degrees of freedom not contacting with water are defined globally. A boundary element formulation describing the acoustic loading on the structure is expressed as a function of normal velocity or displacement on the wetted surface. The coupling of the FEM and BEM is through the normal velocity, or equivalently, the normal displacement on the wetted surface. An acoustical reciprocity is used to prove that the associated acoustic loading expressed as the normal displacement of the wetted structure is a complex symmetric matrix. This matrix can be viewed an acoustic element whose degrees of freedom are the normal displacements of the wetted surface. Thus, the coupled FEM and BEM becomes a symmetric banded matrix formulation, leading to an efficient numerical way to solve the equation. A capped cylindrical shell with periodical ring stiffeners and bulkheads submerged in water is used to demonstrate the present numerical method.