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.

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