Application of Nonlinear Normal Mode Analysis to the Nonlinear and Coupled Dynamics of a Floating Offshore Platform with Damping

Abstract

The nonlinear dynamics of ships and floating offshore platforms has attracted much attention over the last several years. However the topic of multiple-degrees-of-freedom systems has almost been completely ignored with very few exceptions. This is probably due to the complexity of analyzing strongly nonlinear and coupled systems. It turns out that coupling may be particularly important for certain critical dynamics such as the dynamics of a floating offshore platform about its diagonal axis. In a previous work, Kota et al. [1] applied the recently developed nonlinear normal mode technique to analyze the coupled nonlinear dynamics of a floating offshore platform. Although this previous work was restricted to unforced and undamped systems, in this work a comparison of the two alternative nonlinear normal mode analysis techniques was completed. Considering the relative practical importance of damping versus external forcing for this system, in the present work, we utilize just one of the two major techniques available [2] to analyze damped multiple-degrees-of-freedom nonlinear dynamics. Specifically, we investigate the effect of nonlinearity, and non-proportionate damping. Our results show that this technique allows one to simply consider the effect of nonlinearity and general damping on the resulting normal modes. This technique is particularly powerful because it allows one to visualize the modes in a geometric fashion using the invariant manifold concept from dynamical systems.