ABSTRACT

The present paper describes an experimental study of wave-induced chaotic motions of a floating structure with nonlinear moorings. The structure is modeled as a rectangular box, and the moorings are represented by a nonlinear restoring force-displacement relationship corresponding to an idealized geometric nonlinearity associated with a slack mooring or a mooring with gaps. The results are presented in the form of time series, phase portraits, spectra, Poincare maps, and Lyapunov exponents. The influence of various governing parameters on the response is examined. Periodic, sub-harmonic and chaotic responses are observed for both monochromatic and bichromatic waves. In general, sub-harmonic and chaotic responses were obtained for bichromatic excitation to a greater extent than for monochromatic excitation. Transient chaotic motions have also been observed. Poincare maps of the response exhibit a distinct fractal structure under certain conditions, indicating the presence of chaotic motions. Finally, Lyapunov exponents, which provide a quantitative indication of chaotic motions, have also been computed for each time series, and are used to confirm the presence of a chaotic response.

INTRODUCTION

Although a considerable literature on the chaotic response of nonlinear dynamic systems is available, there has been relatively little research reported on chaotic responses in the field of offshore hydrodynamics. One notable example of such responses correspond to the wave-induced motions of a floating structure with nonlinear moorings. Bishop and Virgin (1988) reported on a combined numerical :and geometric approach to modeling the dynamic behavior of a moored semi-submersible, based on solutions of the nonlinear differential equations used to model the system, and observed competing steady states, subharmonic resonance and chaos as typical responses in regular seas. More recently, Aoki, Sawaragi and Isaacson (1993) described a numerical simulation of the motions of a floating body with nonlinear moorings modeled as a single degree of freedom system. They examine the response of systems with both material and geometric nonlinearities to both monochromatic and bichromatic excitation.

You can access this article if you purchase or spend a download.