Singular Mode Characteristics of Fluid-Structure Interaction Modal Formulations

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.