Ocean Engineering

The Motion of Floating Systems: Nonlinear Dynamics in Periodic and Random Waves

[+] Author and Article Information
Katrin Ellermann

Fluid Dynamics and Ship Theory, Hamburg University of Technology, 21071 Hamburg, Germanyellermann@tu-harburg.de

J. Offshore Mech. Arct. Eng 131(4), 041104 (Sep 08, 2009) (7 pages) doi:10.1115/1.3160649 History: Received May 04, 2006; Revised June 11, 2007; Published September 08, 2009

Floating systems, such as ships, barges, or semisubmersibles, show a dynamical behavior, which is determined by their internal structure and the operating conditions caused by external forces e.g., due to waves and wind. Due to the complexity of the system, which commonly includes coupling of multiple components or nonlinear restoring forces, the response can exhibit inherently nonlinear characteristics. In this paper different models of floating systems are considered. For the idealized case of purely harmonic forcing they all show nonlinear behavior such as subharmonic motion or different steady-state responses at constant operating conditions. The introduction of random disturbances leads to deviations from the idealized case, which may change the overall response significantly. Advantages and limitations of the different mathematical models and the applied numerical techniques are discussed.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Model of a floating barge and its mooring system

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Figure 2

Model of a floating crane

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Figure 3

Gaussian distributions for n=1 and n=2

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Figure 4

Overlaying and splitting of distributions. A non-Gaussian probability density (above) is approximated as a sum of Gaussian distributions. The Gaussian distribution with a large variance is split (localized) into the sum of three distributions, each with a smaller variance than the initial distribution.

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Figure 9

Initial distribution for the analysis of the floating crane

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Figure 10

Probability density after three periods of the deterministic part of the forcing

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Figure 11

Mean distribution averaged over three periods of the harmonic component of the forcing t=(5…7) T (T=2π/ω, contour plot). The dark solid line marks the evolution of the corresponding deterministic system.

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Figure 12

Mean distribution averaged over three periods of the harmonic component of the forcing t=(5…7) T(T=2π/ω)

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Figure 5

Time series of coexisting motions

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Figure 6

Phase diagrams of the attractors of the undisturbed system

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Figure 7

Probability density functions for the disturbed system: small perturbation (σ=0.0005)

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Figure 8

Probability density functions for the disturbed system: large perturbation (σ=0.01)

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Figure 13

Mean distribution averaged over the first three periods

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Figure 14

Maxima of the probability density (dots) and trajectory of the deterministically forced system (solid line)



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