Model for Nonlinear Dynamics of Offshore Towers

It is possible to model the responses of deep-ocean tower structures subjected to wave forces. Interactions of four systems—the wave surface heights, the ocean, the hydraulic force, and the structure—lead to a problem formulation involving weakly nonlinear random vibrations. Analytical solution of the problem is achieved by the use of a discrete-system semilinear technique in which an equivalent linear system is studied. Certain coefficient parameters of the equivalent system differential equations of motion are selected in a manner minimizing the error of the equivalent system approximation. Any resulting linear system is nonclassical since normal mode superposition techniques do not apply. Nonclassical mode superposition, which involves complex-valued mode shapes and coordinates, supplies the solution. Principal conclusions are that a simplified analysis (using one nonclassical mode) becomes possible for increasing wind velocities, that amplitude and phasing effects in the various systems require design analyses at many wind velocities, and that form drag forces become noticeable at high wind velocities.