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A linear theory, based on wide-spacing and high-frequency approximations, is developed to describe resonant behaviour in two-dimensional water-wave problems involving a freely floating half-immersed cylinder in the presence of a vertical rigid wall. The theory is not able to describe the lowest-frequency resonance, but otherwise yields explicit approximations for the locations of resonances in the complex plane and for their corresponding residues. Two problems are investigated in detail: the time-domain motion following a vertical displacement of the cylinder from equilibrium, and the time-harmonic motion of a cylinder that is excited by an incident plane wave.
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McIver et al. (2016) studied this question.
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