First- and second-order responses of a floating toroidal structure in long-crested irregular seas
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The first- and second-order heave and pitch motions of a freely floating toroidal body in unidirectional irregular seas are studied using a ring-source boundary integral equation method and a two-term Volterra statistical model. For two different body geometries, added mass and damping coefficients, as well as first- and second-order wave excitations are computed. Since highly tuned resonances of the inner fluid occur at discrete frequencies, second-order wave effects become important when individual incident frequencies or their sum coincide with those natural frequencies. To illustrate this, the second-order sum-frequency rms body motions are computed for three different sea states and compared with the first-order rms motions. Depending on the peak frequency of the input wave spectrum and the parameters of the body geometry, it is shown that the sum-frequency heave and pitch motions can be as large as the first-order motions. These findings have direct implications for the design of toroidal structures such as moonpools, floating breakwaters or pneumatic wave energy absorbers in the ocean. 1993.