Nonlinear Resonant Response of Deep Draft Platforms in Surface Waves

To minimize body motions, floating marine structures are often designed with natural frequencies far away from the spectrum of ocean waves. Such design considerations led to a class of deep draft caisson vessels (DDCV or spars). Even so, large resonant responses may still be generated by excitation from nonlinear interactions of waves with body motions. Past experiments indicated that a DDCV experiences large-amplitude heave and pitch resonant motions when the incident wave frequency is much larger than the heave and pitch natural frequencies. Such resonant motions are not predicted by classical theories without considering nonlinear effects. This nonlinear mechanism has received little attention because of the complex nonlinear wave-body dynamics involved. In this work, we investigate nonlinear wave-wave and wave-body interaction effects on dynamic instability of such marine structures. We first perform a linear stability analysis of the wave-frequency body motion. From the analysis, we find that at certain incident wave frequencies the body motion is unstable with natural heave and pitch motions growing exponentially with time by taking energy from the incident wave through nonlinear wave-body interactions. The condition for the occurrence of instability and the key characteristic features of unstable natural heave and pitch motions, predicted by the analysis, agree well with the experimental measurement and our full-nonlinear numerical simulations. As time-domain fully nonlinear numerical simulations are computationally expensive, we further develop an approximate time-domain analytic model, by including the second-order body nonlinearity only, for predicting the onset of instability and ultimate response of DDCVs in both regular and irregular waves. We use this model to systematically investigate the dependence of unstable motions on frequency detuning, damping, body geometry, and wave parameters.