Time domain modeling of a dynamic impact oscillator under wave excitations

This paper establishes a methodology for analyzing the dynamics of a wave-induced impact model, with emphasis on the modeling of float-over installations. The time domain model described by the Cummins equation provides an attractive way of analyzing the dynamics of marine structures with nonlinear effects. By replacing the time-consuming convolution terms, the resulting model is very efficient in dealing with nonlinear problems. The established time domain model is applied to investigate Leg Mating Unit (LMU) impacts during a float-over operation by considering the heaving motions of the whole system. Both a one-body system (considering that barge and deck move as one rigid body) and a two-body system (barge and deck moving separately) are considered in this paper. The techniques of impact maps, Poincaré maps, bifurcation diagrams and phase portraits are used to investigate the motion characteristics of the barge-deck system undergoing vertical impacts with the substructure.