Modal formulations for linear acoustic and vibration problems are important for model order reduction as well as physical interpretation and insight. In the case of structural acoustic systems, a number of formulations exist for the computation of the modes of the coupled system: these may be referred to as ‘coupled modes’, ‘in-water modes’, etc. These modes have the desirable property that they diagonalize the undamped structural-acoustic problem, making forced-response computations in the time- and frequency-domains trivial. In this paper, we review a number of alternative formulations for the undamped FSI mode problem, and concentrate on a particular aspect: the existence and nature of the singular modes of the systems, i.e. the modes at zero frequency. Corresponding to rigid-body modes in linear elastic systems, these modes are essential for accurate low-frequency performance of reduced-order models. It is found that the original, nonsymmetric system of Zienkiewicz and Newton [53] maintains physically reasonable singular mode properties, while many other formulations do not.

We propose a distributed parallel algorithm for the solution of block circulant linear systems arising from acoustic radiation problems with rotationally symmetric boundary surfaces. When large structural acoustics problems are solved using a coupling finite element/boundary element formulation, the most time consuming part of the analysis is the solution of the linear system of equations for the boundary element computation. In general, the problem is solved frequency by frequency, and the coefficient matrix for the boundary element analysis is fully populated and exhibits no exploitable structure. This typically limits the number of acoustic degrees of freedom to 10–20 thousand. Because acoustic boundary element calculations require approximately six elements per wavelength to produce accurate solutions, the formation is limited to relatively low frequencies. However, when the outer surface of the structure is rotationally symmetric, the system of linear equations becomes block circulant. Building upon a known inversion formula for block circulant matrices, a parallel algorithm for the efficient solution of linear systems arising from acoustic radiation problems with rotationally symmetric boundary surfaces is developed. We show through a runtime, speedup, and efficiency analysis that the reductions in computation time are significant for an increasing number of processors.

Buckling of submerged cylindrical shells is a sudden and rapid implosion which emits a high pressure pulse that may be damaging to nearby structures. The characteristics of this pressure pulse are dictated by various parameters defining the shell structure such as the length to diameter ratio, shell thickness, material, and the existence and configuration of internal stiffeners. This study examines, through the use of high fidelity coupled fluid-structure finite element computations, the impact of various structural parameters on the resulting pressure wave emanating from the implosion. The results demonstrate that certain structural configurations produce pressure waves with higher peak pressure and impulse thereby enhancing the potential for damage to nearby structures.

Recently, a new model for the propagation of sound in interior volumes known as the acoustic diffusion equation has been explored as an alternative method for acoustic predictions and analysis. The model uses statistical methods standard in high frequency room acoustics to compute a spatial distribution of acoustic energy over time as a diffusion process. For volumes coupled through a structural partition, the energy consumed by structural vibration and acoustic energy transmitted between volumes has been incorporated through a simple acoustic transmission coefficient. In this paper, a Boundary Element Method (BEM) solution to the simple diffusion model is developed. The integral form of the 3D acoustic diffusion equation for coupled volumes is derived using the Laplace transform and Green’s Second Identity. The solution using the BEM is developed as well as an efficient Laplace transform inversion scheme to obtain both steady state and transient interior acoustic energy. In addition, a fully coupled model where both structural and acoustic energy are computed as a diffusion process is proposed. A simple volume configuration is examined as the diffusion models are analyzed and compared to conventional room acoustics analysis methods. Advantages of the energy diffusion methods over conventional methods, such as computation of energy distributions and accurate transmission from one volume to another, are revealed as the comparisons are made.

As part of the effort to renew commercial supersonic flight, a predictive numerical tool to compute sonic boom transmission into buildings is under development. Due to the computational limitations of typical numerical methods used at low frequencies (e.g. Finite Element Method), it is necessary to develop a separate approach for the calculation of acoustic transmission and interior radiation at high frequencies. The high frequency approach can then later be combined with a low frequency method to obtain full frequency vibro-acoustic responses of buildings. An analytical method used for the computation of high frequency acoustic transmission through typical building partitions is presented in this paper. Each partition is taken in isolation and assumed to be infinite in dimension. Using the fact that a sonic boom generated far from the structure will approximate plane wave incidence, efficient analytical solutions for the vibration and acoustic radiation of different types of partitions are developed. This is linked to a commercial ray tracing code to compute the high frequency interior acoustic response and for auralization of transmitted sonic booms. Acoustic and vibration results of this high frequency tool are compared to experimental data for a few example cases demonstrating its efficiency and accuracy.