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Research Papers

Stability Analysis of Two-Point Mooring System in Surge Oscillation

[+] Author and Article Information
A. K. Banik1

Department of Civil Engineering, National Institute of Technology, Durgapur, Durgapur 713209, Indiaakbanik@gmail.com

T. K. Datta

Department of Civil Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India

1

Corresponding author.

J. Comput. Nonlinear Dynam 5(2), 021005 (Feb 11, 2010) (8 pages) doi:10.1115/1.4000828 History: Received September 11, 2008; Revised October 01, 2009; Published February 11, 2010; Online February 11, 2010

Nonlinear surge response behavior of a multipoint mooring system under harmonic wave excitation is analyzed to investigate various instability phenomena such as bifurcation, period-doubling, and subharmonic and chaotic responses. The nonlinearity of the system arises due to nonlinear restoring force, which is modeled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc-length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu’s scheme. The period-one and subharmonic solutions obtained by the IHBC method are compared with those obtained by the numerical integration of the equation of motion. Characteristics of solutions from stable to unstable zones, chaotic motion, nT solutions, etc., are identified with the help of phase plots and Poincaré map sections.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Mooring systems: (a) multipoint; (b) two-point taut (β1=0)

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Figure 2

A portion of the equilibrium path

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Figure 3

Frequency response diagram: (a) from a frequency of 0.05 rad/s to 0.5 rad/s (in expanded horizontal scale); (b) from a frequency of 0.5 rad/s to 2 rad/s (in reduced vertical scale)

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Figure 4

Period-one responses at ω=0.89 rad/s (a) phase plot by using the IHB method and NI, and Poincaré map for stable solutions; (b) stable and unstable solutions by IHBC method

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Figure 5

Antisymmetric period-one solutions: ((a) and (b)) phase plot for a dual stable antisymmetric solution at ω=0.4994 rad/s; ((c) and (d)) phase plot for a dual unstable antisymmetric solution at ω=0.45 rad/s; and ((e) and (f)) phase plot for a dual stable antisymmetric solution at ω=0.47 rad/s

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Figure 6

Period-three solutions at ω=0.36 rad/s: (a) phase plot by using the IHB method and NI, and Poincaré map for stable responses; (b) phase plot for stable and unstable responses by using the IHBC method

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Figure 7

Phase plot and Poincaré map for isolated subharmonic responses: (a) period-two motion at ω=0.70 rad/s; (b) period-five motion at ω=0.79 rad/s; (c) period-seven motion at ω=0.63 rad/s; and (d) period-nine motion at ω=0.565 rad/s

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Figure 8

Explosive chaos at ω=0.34 rad/s: (a) phase plot (b) Poincaré section

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Figure 9

Period-doubling route to chaos: (a) period-two motion at ω=0.205 rad/s; (b) period-four motion at ω=0.2045 rad/s; and (c) chaotic responses at ω=0.20 rad/s; (d) Poincaré section

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