Autonomous Oscillations, Bifurcations, and Chaotic Response of Moored Vessels

Abstract

The dynamic behavior of single-point mooring (SPM) systems under time-independent external excitation is analyzed. The time evolution of the corresponding dynamical system is described in a six-dimensional phase space. Bifurcation sequences of state equations are studied and parameter values at which the response of the SPM changes radically are identified. Analysis of stability and instability domains of the system reveals regions of operationally hazardous response. It is shown that an SPM system under time-independent environmental excitation may not stay in a position of static equilibrium. It may start oscillating either periodically or even in a random way depending on the dimension of the attracting set in the phase space, which in general may be noninteger. This explains the large-amplitude slow motions of SPM systems, in the horizontal plane, occasionally observed in practice and often attributed to time-dependent excitation from wave drift forces. Based on these results, rational design decisions can be made for selection of the principal SPM geometric parameters in order to improve the system operability.