Chaotic and Stochastic Dynamics of Offshore Equipment

The chaotic and stochastic dynamics of rocking response of free-standing offshore equipment subjected to horizontal base excitation are investigated using a realistic model taking into account the geometric nonlinearity (finite slenderness ratio) of the rocking systems. Additional important nonlinear effects including transition of governing equations of motion at impact, and abrupt reduction in angular velocity due to impact energy dissipation are examined. It has been demonstrated that the nonlinearities associated with the transition of governing equations at impact procedures complex responses. In addition to the anticipated harmonic and subharmonic periodic responses, two new types of steady state motions - quasi-periodic, and chaotic responses are also found. In this study, it is shown that although the excitations to the rocking systems are simple and purely deterministic, some stochastic characteristics of the chaotic rocking responses are detected using Poincare maps and amplitude probability densities. While the chaotic time histories have a periodic time dependency, thus non-stationary, time series consist of Poincare points are ergodic. Results indicate that chaotic response may be a strong link between deterministic and stochastic responses.