Experimental investigation of response stability and transition behaviour of a nonlinear ocean structural system

Abstract

This study experimentally investigates the nonlinear response stability and transition behaviour of a submerged, moored ocean structural system which consists of a spherical buoy and attached multi-point mooring lines. The system is excited by a periodic wave field in a closed channel. System nonlinearities include complex geometric restoring (stiffness) force and coupled fluid–system interaction exciting forces. Experimental set-up, operating procedures and analysis of the measured results are presented. Characteristic motions observed include harmonic, subharmonic and ultraharmonic responses, which demonstrate a signature of the intricate pattern of the nonlinear global behaviour. Good agreements between the measured and most predicted responses are demonstrated in both time and frequency domains. These results confirm the validity of the analytical model presented and calibrate the accuracy of the existing numerical predictions. Primary and secondary resonances in the response are identified via frequency response curves. Response bifurcation cascades are observed in the experimental results and the possible existence of higher-order nonlinear responses is inferred.

Introduction

Analytical and numerical models of nonlinear systems subjected to periodic excitation have revealed a variety of nonharmonic responses, instabilities and sensitivity to initial conditions (e.g. Moon, 1987, Moon, 1992). These predictions have been demonstrated through small-scale experiments where the system parameters can be accurately controlled, and the domains of attraction are easily defined and measured. Examples of these `table-top' experiments of nonlinear aperiodic responses can be found in Moon (1987), Moon (1992). Other examples of small-scale experimental investigations of simple single- and two-degree-of-freedom systems are reported in Popp and Stelter (1990) and Nayfeh and Balachandran (1990), respectively.

However, it may be difficult to design large-scale models to obtain chaotic responses. To the authors' knowledge to date, a large-scale fluid-structure experiment to obtain highly sensitive, nonlinear response (e.g. chaos) in the ocean has not yet been achieved. While there is an expansive amount of material on nonlinear fluid–structure interaction in the literature (e.g. Sarpakaya and Isaacson, 1981, Blevins, 1990) describing harmonic small-amplitude motions, there are only a few papers describing subharmonic responses (e.g. Lean, 1971, Thompson et al., 1984, Fujino and Sagara, 1990).

A medium-scale experimental investigation of the nonlinear response of a submerged, moored, complex ocean system is reported here. The objective of this study is two-fold: (i) to experimentally determine, as much as possible, the existence of nonlinear responses (e.g. subharmonic, ultraharmonic, ultrasubharmonic, quasi-periodic and chaotic, similar to those predicted in Gottlieb and Yim, 1992), and the organized response transition in bifurcation sets predicted in the analytical study (Gottlieb et al., 1997); and (ii) to assess the validity of the analytical model of a symmetric multi-point moored structural system subjected to a deterministic exciting field described by small amplitude waves and weak collinear current. The study presents a description of the submerged, moored ocean system experiment, classification of model responses and comparison of results to analytical predictions.