A Systematic Approach to Modeling Nonlinear Multi-DOF Ship Motions in Regular Seas

Chen, Shyh Leh; Shaw, Steven W.; Troesch, Armin W.

doi:10.5957/jsr.1999.43.1.25

Cited by 12 publications

(2 citation statements)

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“…[16] derived realistic hydrodynamic coefficients to analyze the nonlinear dynamics of planning hulls, and they discovered instabilities and bifurcations. Chen, et al [17] developed a systematic technique for modeling nonlinear ship dynamics in a very comprehensive and outstanding study. However, their focus is on roll, sway, and heave, which is of limited relevance for our current problem.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of yaw motion of surface vehicles

Kambali

Nataraj

2022

Nonlinear Dyn

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The dynamics of surface vehicles such as boats and ships, when modeled as a rigid body, is complex as it is strongly nonlinear and involves six degrees of freedom. We are particularly interested in the steering dynamics decoupled from pitching and rolling as the basis of our research on unmanned boats and autonomy. Steering dynamics has been traditionally modeled using a linear Nomoto model, which however does a poor job of capturing real nonlinear phenomena. On the other hand, there exists a somewhat simplified three degree of freedom nonlinear model derived by Abkowitz, which, although better than the Nomoto model, is still too intractable for analytical methods. In this paper, we derive a nonlinear single degree of freedom model with a cubic nonlinearity that is conditionally equivalent to the Abkowitz model. Using this model we analyze the yaw motion of an autopilot ship with a PD controller under the influence of an external wave force.Analytical and numerical investigations of the nonlinear dynamics are performed using parameters of an example container ship for various sea states. We employ the harmonic balance method to investigate the nonlinear frequency response of the ship under the influence of different parameters and demonstrate that the external wave force is balanced by stiffer ships. We also numerically investigate the nonlinear dynamic behavior to understand the different mechanisms involved in transitions from periodic to chaotic behavior under the influence of various parameters and different sea state conditions. The analysis reveals periodic response of the ship for a calm sea state. It is noteworthy that for lower values of linear stiffness, higher values of nonlinear stiffness, and higher values of external wave force corresponding to higher sea states, the bifurcation structure reveals mixed dynamic response in which periodic solutions evolve into period doubled, period tripled, and chaotic like solutions even with high levels of damping. This work aims to demonstrate the utility of a simple nonlinear model and nonlinear behavior of

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of yaw motion of surface vehicles

Kambali

Nataraj

2022

Nonlinear Dyn

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“…A reduction in the degrees of freedom results in more idealized models, and often allows for a more rigorous analysis that yields mathematical results in terms of the system parameters. Such reductions can, in many cases, be mathematically justi ed using invariant manifold theory, as demonstrated by Chen et al . (1999).…”

Section: Introductionmentioning

confidence: 99%

Capsize criteria for ship models with memory-dependent hydrodynamics and random excitation

Jiang

Troesch

Shaw

2000

Philosophical Transactions of the Royal Society of London. Seri

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The large-amplitude rolling and capsize dynamics of vessels in random beam seas are investigated using a nonlinear single-degree-of-freedom model. Included in this model are three types of damping moments|the usual e¬ects that are treated as linear and quadratic in the roll velocity, plus a frequency-dependent e¬ect that captures the dissipation of energy caused by the generation of waves radiated away from the rolling vessel. The description of this type of damping requires a history-dependent term in the equations of motion. This memory e¬ect prevents a straightforward application of the standard Melnikov method for determining capsize criteria. In this work, the Melnikov function and phase-space transport techniques are extended to derive a criterion for capsizing that can be applied to analytical models with this type of damping. Using these theoretical results, we obtain a closed-form asymptotic expression for a critical signi cant wave height, and this criterion is evaluated using simulation studies for a realistic set of vessel parameters.

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Melnikov’s Method for Ship Motions without the Constraint of Small Linear Damping

McCue

IUTAM Symposium on Fluid-Structure Interaction in Ocean Engineering

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A Systematic Approach to Modeling Nonlinear Multi-DOF Ship Motions in Regular Seas

Cited by 12 publications

References 0 publications

Nonlinear dynamics of yaw motion of surface vehicles

Nonlinear dynamics of yaw motion of surface vehicles

Capsize criteria for ship models with memory-dependent hydrodynamics and random excitation

Melnikov’s Method for Ship Motions without the Constraint of Small Linear Damping

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