Computing fluid-coupled resonance frequencies, mode shapes, and damping loss factors using the singular value decomposition

In many acoustic design problems, it would be useful to be able to compute fluid-coupled resonance frequencies, mode shapes, and their associated damping levels. Unfortunately, conventional eigenvalue solution procedures are either computationally inefficient, unreliable, or have limited applicability. Sophisticated methods for identifying modal parameters using the singular value decomposition have recently emerged in the area of experimental modal analysis, where the available data typically consists of velocity-to-force transfer functions for several drive point locations. In this paper, we show that these techniques can be applied to numerically generated frequency domain data and are even more effective because full matrices of transfer function data are available. This typically allows the modes to be completely separated from each other, such that the modal parameters can be identified using analytical formulas. Several benchmark example problems are solved numerically, including a rectangular cantilever plate, a baffled circular plate, and a baffled circular plate covered by an open-ended rigid-walled pipe.