A modal decomposition technique to analyze individual modal contributions to the sound power radiated from an externally excited structure submerged in a heavy fluid is presented. The fluid-loaded structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem. The eigenvalues and eigenfunctions of a fluid loaded sphere with and without internal structures are presented. The modal sound power contributions using both fluid-loaded structural modes and acoustic radiation modes are presented. The results for the resistive and reactive sound power obtained from the superposition of the individual modal sound power contributions are compared to the harmonic solution of the forced problem.

SUMMARY Fully coupled finite element/boundary element models are a popular choice when modelling structures that are submerged in heavy fluids. To achieve coupling of subdomains with non‐conforming discretizations at their common interface, the coupling conditions are usually formulated in a weak sense. The coupling matrices are evaluated by integrating products of piecewise polynomials on independent meshes. The case of interfacing elements with linear shape functions on unrelated meshes has been well covered in the literature. This paper presents a solution to the problem of evaluating the coupling matrix for interfacing elements with quadratic shape functions on unrelated meshes. The isoparametric finite elements have eight nodes (Serendipity) and the discontinuous boundary elements have nine nodes (Lagrange). Results using linear and quadratic shape functions on conforming and non‐conforming meshes are compared for an example of a fluid‐loaded point‐excited sphere. It is shown that the coupling error decreases when quadratic shape functions are used. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents a method to identify the surface areas of a vibrating structure that contribute to the radiated sound power. The surface contributions of the structure are based on the acoustic radiation modes and are computed for all boundaries of the acoustic domain. The surface contributions are compared to the acoustic intensity, which is a common measure for near-field acoustic energy. Sound intensity usually has positive and negative values that correspond to energy sources and sinks on the surface of the radiating structure. Sound from source and sink areas partially cancel each other and only a fraction of the near-field acoustic energy reaches the far-field. In contrast to the sound intensity, the surface contributions are always positive and no cancelation effects exist. The technique presented here provides a method to localize the relevant radiating surface areas on a vibrating structure. To illustrate the method, the radiated sound power from a baffled square plate is presented.

A numerical technique for modal decomposition of the acoustic responses of structures submerged in a heavy fluid medium using fluid-loaded structural modes is presented. A Krylov subspace model order reduction approach to reduce the computational effort required for a fully coupled finite element/boundary element model is described. By applying the Krylov subspace to only the structural part of the global system of equations for the fully coupled problem, only the frequency independent finite element matrices are reduced. A fluid-loaded cylindrical shell closed at each end by hemispherical end caps is examined. The cylinder is excited by a ring of axial or transverse forces acting at one end. The individual contributions of the cylinder circumferential modes to the sound power and directivity of the radiated sound pressure are observed. The technique presented here provides a tool for greater physical insight into exterior acoustic-structure interaction problems using fully coupled numerical models, with significantly reduced computational effort.

By identifying the efficiently radiating acoustic radiation modes of a fluid loaded vibrating structure, the storage requirements of the acoustic impedance matrix for calculation of the sound power using the boundary element method can be greatly reduced. In order to compute the acoustic radiation modes, the impedance matrix needs to be symmetric. However, when using the boundary element method, it is often found that the impedance matrix is not symmetric. This paper describes the origin of the asymmetry of the impedance matrix and presents a simple way to generate symmetry. The introduction of additional errors when symmetrizing the impedance matrix must be avoided. An example is used to demonstrate the behavior of the asymmetry and the effect of symmetrization of the impedance matrix on the sound power. The application of the technique presented in this work to compute the radiated sound power of a submerged marine vessel is discussed.