Small amplitude vibrations of a structure completely filled with a fluid are considered.\nDescribing the structure by displacements and the fluid by its pressure field, the free vibrations\nare governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for\ntaking advantage of the structure of the non-symmetric eigenvalue problem allowing for a variational\ncharacterization of its eigenvalues. Structure-preserving iterative projection methods of the the\nArnoldi and of the Jacobiââ?¬â??Davidson type and an automated multi-level sub-structuring method are\nreviewed. The reliability and efficiency of the methods are demonstrated by a numerical example
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