ISSN:
1573-269X
Keywords:
Heave-roll coupling
;
parametric excitation
;
bifurcation
;
instability region
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A nonlinear model for simulating the heave-roll motions of ships in following waves is presented. The parametric excitation is modeled by a Hill's type equation, instead of the conventional Mathieu's equation. The model includes not only the linear but also the quadratic coupling term. Instability conditions for parametrically excited rolling motions are derived using the harmonic balance method. The results are verified by numerical analyses. The effects of including the quadratic coupling term on the instability conditions and nonlinear responses are studied. The complex dynamic behaviour of the coupled system in the various instability regions is also investigated. Bifurcations of the flip, fold and pitchfork types are observed in the Poincaré mapping of the numerically simulated responses. Chaotic motions leading to boundary crises and inevitable capsize are also reported.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00045774
