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Trapped modes in the linearized water-wave problem are free oscillations of an unbounded fluid with a free surface that have finite energy; it has been known for some time that such modes are supported by certain structures when held fixed. This paper investigates the problem of a freely floating structure that is able to move in response to the hydrodynamic forces acting upon it and it is shown that trapped modes also exist in this problem. For a freely floating structure, a trapped mode is a coupled oscillation of the fluid and the structure.
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McIver et al. (2006) studied this question.
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