Modeling of Ship Roll Dynamics and Its Coupling with Heave and Pitch
In order to study the dynamic behavior of ships navigating in severe environmental conditions it is imperative to develop their governing equations of motion taking into account the inherent nonlinearity of large-amplitude ship motion. The purpose of this paper is to present the coupled nonlinear equations of motion in heave, roll, and pitch based on physical grounds. The ingredients of the formulation are comprised of three main components. These are the inertia forces and moments, restoring forces and moments, and damping forces and moments with an emphasis to the roll damping moment. In the formulation of the restoring forces and moments, the influence of large-amplitude ship motions will be considered together with ocean wave loads. The special cases of coupled roll-pitch and purely roll equations of motion are obtained from the general formulation. The paper includes an assessment of roll stochastic stability and probabilistic approaches used to estimate the probability of capsizing and parameter identification.
Global Dynamics of Froude-Type Oscillators with Superlinear Damping Terms
This paper deals with the damped superlinear oscillator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x'' + a(t)\phi_p\bigl(x' \bigr) + b(t)\phi_q\bigl(x'\bigr)+ \omega^2x = 0, $$\end{document} where a(t) and b(t) are continuous and nonnegative for t≥0; p and q are real numbers greater than or equal to 2; ϕr(x′)=|x′|r−2x′. This equation is a generalization of nonlinear ship rolling motion with Froude’s expression, which is very familiar in marine engineering, ocean engineering and so on. Our concern is to establish a necessary and sufficient condition for the equilibrium to be globally asymptotically stable. In particular, the effect of the damping coefficients a(t), b(t) and the nonlinear functions ϕp(x′), ϕq(x′) on the global asymptotic stability is discussed. The obtained criterion is judged by whether the integral of a particular solution of the first-order nonlinear differential equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u' + \omega^{p-2}a(t)\phi_p(u) + \omega^{q-2}b(t)\phi_q(u) + 1 = 0 $$\end{document} is divergent or convergent. In addition, explicit sufficient conditions and explicit necessary conditions are given for the equilibrium of the damped superlinear oscillator to be globally attractive. Moreover, some examples are included to illustrate our results. Finally, our results are extended to be applied to a more complicated model.
Numerical analysis and experimental observation of guidewire motion in a blood vessel model.
We have developed a computer-based system to simulate a guidewire in blood vessels for surgical planning, intra-operative assistance, and to facilitate the design of new guidewires. In this study, we compared simulation results with experimental results for validation of the simulation system. First, we inserted a commercial guidewire into a poly (vinyl alcohol) hydrogel blood vessel model using a two-axis automatic stage and measured the position of the guidewire tip and the contact force between the guidewire and the vessel. The experimental apparatus can be used not only for the validation of numerical analyses, but also as a simulation system. Second, similarly to the experiment, the motion of the guidewire in the blood vessel model was calculated when the proximal part of the guidewire model was pushed and twisted. The model of the guidewire is constructed with viscoelastic springs and segments, and the proximal part of the guidewire model is constrained by the fixed catheter model. Collisions between the guidewire and the vessel are calculated, and the contact forces are determined according to the stiffness of the vessel wall. The same tendency was seen in the trajectories and the contact force of both the experimental and simulated guidewire tips.