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TECHNICAL PAPERS

Routes to Large Amplitude Motions of Mooring Systems Due to Slowly Varying Drift

[+] Author and Article Information
João Paulo J. Matsuura

Department of Naval Architecture and Marine Engineering, The University of Michigan, 2600 Draper Road, Ann Arbor, MI 48109-2145matsuura@engin.umich.edu

Michael M. Bernitsas

Department of Naval Architecture and Marine Engineering, The University of Michigan, 2600 Draper Road, Ann Arbor, MI 48109-2145michaelb@engin.umich.edu

J. Offshore Mech. Arct. Eng 128(4), 280-285 (Mar 27, 2006) (6 pages) doi:10.1115/1.2217752 History: Received November 15, 2004; Revised March 27, 2006

The effect of second-order slowly varying wave drift (SVWD) forces on the horizontal plane motions of moored floating vessels has been studied for nearly 30 years. Large amplitude oscillations of moored vessels have been observed in the field or predicted numerically. Often, those have been incorrectly attributed to resonance or time-varying excitation from current/wind. In previous work, the authors have shown that resonance is only one of numerous interaction phenomena, and that large amplitude oscillations can be induced by SVWD forces or even time-independent excitation. Currently, there is no mathematical theory to study stability and bifurcations of mooring systems subjected to nonautonomous spectral excitation. Thus, in this paper, bifurcation boundaries are approximated by analyzing simulation data from a grid of points in the design space. These boundaries are plotted in the catastrophe sets of the corresponding autonomous system, for which a design methodology has been developed at the University of Michigan since 1985. This approach has revealed a wealth of dynamics phenomena, characterized by static (pitchfork) and dynamic (Hopf) bifurcations. Interaction of SVWD forces with the Hopf bifurcations may result in motions with amplitudes 2–3 orders of magnitude larger than those due to resonance. On the other hand, in other cases the SVWD/Hopf interaction may reduce or even eliminate limit cycles.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 4

Four-line TMS catastrophe set: H1∕3=3.66m(12ft), chains, T-M

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Figure 5

Yaw angle, design point D4, H1∕3=1.83m(6ft): xp∕L=0.44, θ=225deg

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Figure 6

Yaw angle, design point D5, H1∕3=3.66m(12ft): xp∕L=0.44, θ=180deg

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Figure 7

Yaw angle, design point D8, H1∕3=3.66m(12ft): xp∕L=0.42, θ=202.5deg

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Figure 8

Yaw angle, design point D9, H1∕3=1.83m(6ft): xp∕L=0.365, θ=225deg

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Figure 9

Yaw angle, design point D10, H1∕3=3.66m(12ft): xp∕L=0.39, θ=202.5deg

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Figure 10

Yaw angle, design point D11, H1∕3=3.66m(12ft): xp∕L=0.52, θ=180deg

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Figure 11

Yaw angle, design point D12, H1∕3=3.66m(12ft): xp∕L=0.49, θ=180deg

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Figure 12

Yaw angle, design point D13, H1∕3=1.83m(6ft): xp∕L=0.35, θ=225deg

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Figure 13

Yaw angle, design point D13, H1∕3=3.66m(12ft): xp∕L=0.35, θ=225deg

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Figure 3

Four-line TMS catastrophe set: H1∕3=1.83m(6ft), chains, T-M

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Figure 1

Geometry of a spread mooring system (SMS)

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Figure 2

Four-line TMS catastrophe set: Chains, T-M

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