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Catchment Regions of Multiple Dynamic Responses in Nonlinear Problems of Offshore Mechanics

Publication ,  Journal Article
Virgin, LN; Bishop, SR
Published in: Journal of Offshore Mechanics and Arctic Engineering
January 1, 1990

Consideration of nonlinear effects in the dynamic analysis of offshore structures leads to complex phenomena even for relatively simple deterministic mathematical models. Nonlinearity in the stiffness or restoring force of a structure can be conveniently incorporated into a differential equation of motion, which can then be solved either analytically, using perturbation techniques, or numerically for various parameter ranges and forcing conditions. A particular feature of nonlinear dynamics is the appearance of multiple, competing steady-state oscillations which depend crucially on initial conditions. These coexisting stable solutions can be thought of as attractors for transient motion. A central question is therefore: How does the final long-term behavior of a dynamical system depend on the starting conditions? This paper concentrates on the computation of the domains of attraction or catchment regions using numerical techniques based on Poincare mapping ideas. The three specific examples illustrated are the roll motion of a ship, the oscillations of an articulated column and the surge response of a moored semi-submersible. This work may be considered an extension of previous work by the same authors. © 1990 by ASME.

Duke Scholars

Published In

Journal of Offshore Mechanics and Arctic Engineering

DOI

EISSN

1528-896X

ISSN

0892-7219

Publication Date

January 1, 1990

Volume

112

Issue

2

Start / End Page

127 / 133

Related Subject Headings

  • Energy
  • Civil Engineering
  • 0914 Resources Engineering and Extractive Metallurgy
  • 0913 Mechanical Engineering
  • 0911 Maritime Engineering
  • 0905 Civil Engineering
 

Citation

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ICMJE
MLA
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Virgin, L. N., & Bishop, S. R. (1990). Catchment Regions of Multiple Dynamic Responses in Nonlinear Problems of Offshore Mechanics. Journal of Offshore Mechanics and Arctic Engineering, 112(2), 127–133. https://doi.org/10.1115/1.2919846
Virgin, L. N., and S. R. Bishop. “Catchment Regions of Multiple Dynamic Responses in Nonlinear Problems of Offshore Mechanics.” Journal of Offshore Mechanics and Arctic Engineering 112, no. 2 (January 1, 1990): 127–33. https://doi.org/10.1115/1.2919846.
Virgin LN, Bishop SR. Catchment Regions of Multiple Dynamic Responses in Nonlinear Problems of Offshore Mechanics. Journal of Offshore Mechanics and Arctic Engineering. 1990 Jan 1;112(2):127–33.
Virgin, L. N., and S. R. Bishop. “Catchment Regions of Multiple Dynamic Responses in Nonlinear Problems of Offshore Mechanics.” Journal of Offshore Mechanics and Arctic Engineering, vol. 112, no. 2, Jan. 1990, pp. 127–33. Scopus, doi:10.1115/1.2919846.
Virgin LN, Bishop SR. Catchment Regions of Multiple Dynamic Responses in Nonlinear Problems of Offshore Mechanics. Journal of Offshore Mechanics and Arctic Engineering. 1990 Jan 1;112(2):127–133.

Published In

Journal of Offshore Mechanics and Arctic Engineering

DOI

EISSN

1528-896X

ISSN

0892-7219

Publication Date

January 1, 1990

Volume

112

Issue

2

Start / End Page

127 / 133

Related Subject Headings

  • Energy
  • Civil Engineering
  • 0914 Resources Engineering and Extractive Metallurgy
  • 0913 Mechanical Engineering
  • 0911 Maritime Engineering
  • 0905 Civil Engineering