Optimal control of wave-induced vibrations in semisubmersible structures with flexible superstructures

This dissertation is concerned with controlling the motion of a semisubmersible structure induced by high-frequency waves. The structure consists of a rigid platform and a flexible superstructure. Motion of a structure in fluids generates forces depending on the motion itself. The added mass and damping terms stemming from this motion depend on the frequency of motion. It is well known that for a given wave height, the wave energy is distributed according to a Rayleigh distribution. Because mass and damping terms vary with the frequency of the wave motion, there is an infinite number of sets of dynamical equations, one for each frequency in the Rayleigh distribution. Practical considerations make it necessary to discretize the frequency spectrum, so that there are as many dynamical equations as frequency increments. The center frequency in each increment is computed by equipartitioning of the wave energy distribution represented by a Bretschneider spectrum. The excitation forces are estimated for each increment and the design of optimal control is carried out by the Independent Modal-Space Control (IMSC) method. The net control forces can be found by summing the forces associated with each increment. The technique is demonstrated by means of a numerical example in which the wave-induced vibration of a cylindrical platform with a flexible cantilever beam is suppressed.