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Chaotic motions of nonlinearly moored structures Phadke, Amal C.


A number of studies have described the theoretical and numerical aspects of the chaotic motions of offshore structures with nonlinear moorings. As one such example, Aoki, Sawaragi and Isaacson (1993) described the numerical simulation of the motions of a single degree of freedom system with a piecewise-linear restoring force function. However, relatively few laboratory measurements of chaotic motions have been reported, and the primary aim of the present study is to investigate the corresponding problem experimentally. Thus, the present work describes the measurement of 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 experiments were conducted in the wave flume of the Hydraulics Laboratory of the Department of Civil Engineering at the University of British Columbia. The flume is 40 m long, 0.62 m wide, operates with a nominal water depth of 0.55 m, and is equipped with a wave generator capable of producing regular and random waves and controlled by a DECVAXstation-3200 computer. The model structure is 76 cm long x 25 cm wide x 20 cm high. Two vertical Plexiglas plates parallel to the sides of the wave flume were installed so as to limit the structure motions to three degrees of freedom corresponding to surge, heave and pitch. Ball bearings mounted on the sides of the box are used to minimize friction between the plates and the structure. Two vertical cantilevered beams located at some distance from the each end of the structure were used to simulate the nonlinear mooring stiffness. Displacement measurements at three different locations on the body were made using potentiometers mounted on a rigid aluminum frame, with a system of strings, pulleys and counter-weights used to transmit the structure motions to the potentiometers. The measured displacements were transformed to provide the surge, heave and pitch motions with respect to the centre of gravity of the structure. 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. These include a dimensionless wave height, which characterizes the magnitude of the excitation; a relative wave frequency; and gap width and a dimensionless spring stiffness, which characterize the moorings. Periodic, sub-harmonic and chaotic responses are observed for both monochromatic and bichromatic waves. In general, sub-harmonic and chaotic responses were obtained forbichromatic excitation to a greater extent than for monochromatic excitation. Transient chaotic motions have also been observed, such that the response initially appears to be very irregular, but eventually settles to a regular periodic motion. Poincart 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 chaotic motions.

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