Asymmetric Dynamic Systems Research Articles

Stability and capsizing analysis of nonlinear ship rolling in wind and stochastic beam seas

Considering the actual seaway condition, stability and capsizing of nonlinear ship rolling system in stochastic beam seas is of significant importance for voyage safety. Safe zone are defined in the phase space plan of the unperturbed Hamilton system to qualitatively distinguish ship motions as capsize and noncapsize. Capsize events are defined by solutions passing out of the safe zone. The probability of such an occurrence is studied by virtue of the random Melnikov function and the concept of phase space flux. In this paper, besides conventional wave excitation, the effect of wind load is also taken into account. The introduction of wind load will lead to asymmetry, in other words, it transforms the symmetric heteroclinic orbits into asymmetric homoclinic orbits. For asymmetric dynamical system, the orbital analytic solutions and its power spectrum are not readily available, and the technique of discrete time Fourier transformation (DTFT) is used. In the end, as verification of theoretical critical significant wave height, capsizing probability contour diagram is generated by means of numerical simulation. The contour diagram shows that these analytical methods provide reliable and predictive results about the likelihood of a vessel capsizing in a given seaway condition.

Chaos Research of Asymmetric System Based on Melnikov Method

Based on Helmholtz-Duffing which is a typical nonlinear asymmetric dynamical system, According to homoclinic bifurcations, prerequisites for chaos motion are obtained by use of Melnikov theory. As a result of verifying the analytic solutions, the safe basin and the phenomena of erosion of the safe basin are simulated by numerical method in the end. The research indicates that the value range of is closely related to the area influenced by the value itself: when is located in the range of from zero to one, the left part of system is mainly affected; when is larger than one, the right part of system is mainly affected. For the same symmetry parameter , there exist a critical frequency at which the threshold value of the amplitudes of both left and right part of system are equal.

A hybrid control approach for pole assignment to second-order asymmetric systems

Structural modification in the form of adding mass and stiffness (and sometime damping) as a means of passive control to assign desirable poles and zeros for symmetric systems has been extensively studied. Pole and zero assignment by means of active control has also attracted much research. Assignment of poles to stabilise second-order damped asymmetric dynamic systems using structural modifications and state-feedback control, respectively, was carried out recently. It was found that the former is often incapable of assigning complex poles with negative real parts for asymmetric systems while the latter is nearly always capable of doing that. However, the gains required to assign poles with negative real parts using active control can be high. This paper presents a two-stage passive (structural modification) and active (state-feedback) combined control approach to assign complex poles with negative real parts to damped asymmetric dynamic systems to suppress flutter instability. This hybrid approach is motivated by possible restriction to gains of actuators and cost of sole active control. Simulated numerical examples show its effectiveness over the individual control strategies of passive control and active control.

New Riddling Bifurcation in Asymmetric Dynamical Systems

We investigate the bifurcation mechanism for the loss of transverse stability of the chaotic attractor in an invariant subspace in an asymmetric dynamical system. It is found that a direct transition to global riddling occurs through a transcritical contact bifurcation between a periodic saddle embedded in the chaotic attractor on the invariant subspace and a repeller on its basin boundary. This new bifurcation mechanism differs from that in symmetric dynamical systems. After such a riddling bifurcation, the basin becomes globally riddled with a dense set of repelling tongues leading to divergent orbits. This riddled basin is also characterized by divergence and uncertainty exponents, and typical power-law scaling is found.