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TECHNICAL PAPERS

A Numerical Feasibility Study of a Parametric Roll Advance Warning System

[+] Author and Article Information
Leigh Shaw McCue

Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061mccue@vt.edu

Gabriele Bulian

Department of Naval Architecture, Ocean and Environmental Engineering (DINMA), University of Trieste, Trieste, Italygbulian@units.it

As described in Sec. 2, according to experimental data, the analytical model described leads to an overestimation of roll; therefore, the results presented for a simulated significant wave height of 2.644m correspond to experimental cases nearer a significant wave height of 3.7m.

J. Offshore Mech. Arct. Eng 129(3), 165-175 (Jan 23, 2007) (11 pages) doi:10.1115/1.2746399 History: Received July 02, 2006; Revised January 23, 2007

This work studies the practicality of using finite-time Lyapunov exponents (FTLEs) to detect the inception of parametric resonance for vessels operating in irregular longitudinal seas. Parametrically excited roll motion is modeled as a single-degree-of-freedom system, with nonlinear damping and restoring terms. FTLEs are numerically calculated at every integration time step. Using this numerical model of parametric roll and through tracking trends in the FTLE time series behavior, warnings of parametric roll are identified. This work serves as a proof of concept of the FTLE technique’s viability in detecting parametric resonance. The ultimate aim of the research contained in this paper, along with future work, is the development of a real-time, onboard aid to warn of impending danger allowing for avoidance of severe, even catastrophic, vessel instabilities.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Effective wave amplitude spectrum from Bretschneider spectrum with modal frequency ωm=0.683 and H1∕3∕Lpp=1∕50

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Figure 3

Sample parametric roll time histories for TR2 subject to waves defined by Bretschneider spectrum with ωm=0.683 and H1∕3∕Lpp=1∕50 for Fn=0.04

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Figure 4

Histogram of maximum FTLEs separated by runs experiencing, and not experiencing roll in excess of 30deg as simulated over 500s for Fn=0.04

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Figure 5

Roll time history (top), finite-time Lyapunov exponent time history (middle), sum of FTLE time history (bottom) for first case in Fig. 3 for Fn=0.04

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Figure 6

Magnification near first parametric roll event in Fig. 5 for Fn=0.04

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Figure 7

Sample parametric roll time histories for TR2 subject to waves defined by Bretschneider spectrum with ωm=0.683 rad/s and H1∕3∕Lpp=1∕50 for Fn=0.0

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Figure 8

Roll time history (top), finite-time Lyapunov exponent time history (middle), sum of FTLEs time history (bottom) for first case in Fig. 7 for Fn=0.0

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Figure 9

Magnification near first parametric excitation in Fig. 8 for Fn=0.0

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Figure 10

Numerical and theoretical dependence of SFTLEs on roll velocity

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Figure 11

Roll time history (top), finite-time Lyapunov exponent time history (middle), sum of FTLE time history (bottom) for case leading to capsize for Fn=0.04

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Figure 12

Magnified portions of FTLE time series from Fig. 1 for case leading to capsize for Fn=0.04

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Figure 13

Roll-roll velocity phase space of time series from Fig. 1 for case leading to capsize for Fn=0.04

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Figure 14

Angle of static vanishing stability ϕv as a function of the effective wave amplitude

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Figure 15

Histogram of maximum FTLEs separated by runs capsizing or not capsizing as simulated over 1000s for Fn=0.04

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Figure 16

Histogram of time from maximum ftle to capsize over 1000s for Fn=0.04

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