Vibro-Impact Interaction of Ships With Ice

2008 ◽  
Author(s):  
I. F. Grace ◽  
R. A. Ibrahim
Keyword(s):  
Initial Conditions ◽  
Excitation Amplitude ◽  
Basins Of Attraction ◽  
Analytical Models ◽  
Safe Operation ◽  
Rigid Barrier ◽  
Impact Interaction ◽  
Different Response ◽  
Motion Period ◽  
Impact Motion

Impact dynamic interaction of ships with solid ice or stationary rigid structures is a serious problem that affects the safe operation and navigation in arctic regions. The purpose of this study is to present two analytical models of impact interaction between ship roll dynamics and one-side rigid barrier. These models are the phenomenological modeling represented by a power law in stiffness and damping forces, and Zhuravlev non-smooth coordinate transformation. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequencies of external wave roll moment. The basins of attraction of safe operation are obtained and reveal the coexistence of different response regimes such non-impact periodic oscillations, modulation impact motion, period added impact oscillations, chaotic impact motion and unbounded rotational motion. The results are summarized in the bifurcation diagram in terms of response amplitude-excitation amplitude plane.

Modelling and analysis of ship roll oscillations interacting with stationary icebergs

2008 ◽  
Vol 222 (10) ◽  
pp. 1873-1884 ◽  
Author(s):  
I F Grace ◽  
R A Ibrahim
Keyword(s):  
Initial Conditions ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Basins Of Attraction ◽  
Analytical Models ◽  
Safe Operation ◽  
Rigid Barrier ◽  
Ship Roll ◽  
Different Response ◽  
Impact Motion

Impact dynamic interaction of ships with solid ice or stationary rigid structures is a serious problem that affects the safe operation and navigation in arctic regions. The purpose of this study is to present two analytical models of impact interaction between ship roll dynamics and one-side rigid barrier. These models are the phenomenological modelling represented by a power law in stiffness and damping forces, and Zhuravlev non-smooth coordinate transformation. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequencies of external wave roll moment. The basins of attraction of safe operation are obtained and reveal the coexistence of different response regimes such as non-impact periodic oscillations, modulation impact motion, period-added impact oscillations, chaotic impact motion, and unbounded rotational motion. The results are summarized in the bifurcation diagram in terms of response-excitation amplitudes plane. The stability fraction index is obtained for different values of excitation frequency based on the ratio of the area of bounded roll oscillations to the total area of the grazing orbit.

Study of vehicle crashes into a rigid barrier

2020 ◽  
Vol 44 (3) ◽  
pp. 335-343 ◽  
Author(s):  
Robert Kostek ◽  
Piotr Aleksandrowicz
Keyword(s):  
Computer Simulation ◽  
Initial Conditions ◽  
Closed Circuit ◽  
Crash Test ◽  
Accident Reconstruction ◽  
Rigid Barrier ◽  
Closed Circuit Television ◽  
Post Impact ◽  
Simulation Results ◽  
Impact Motion

This study presents the results of both a computer simulation of a vehicle crash into a rigid barrier obtained with V-SIM4 software and an experimental crash test published by ADAC (Allgemeiner Deutscher Automobil-Club). The results were obtained using the same initial conditions, which provides an opportunity to compare results and evaluate the reliability of simulation results. Observed errors and adopted models are discussed. The sensitivity of the post-impact motion to the overlap and engaged gear was studied, which is a result of non-linear phenomena occurring during the crashes. Expert witnesses (accident reconstructionists) often face such problems. Consequently, the important factor of any accident reconstruction is the knowledge of the expert and the identification of pre-impact conditions, which are uncertain. This study also addresses practical issues related to traffic collision reconstruction, employment of CCTV (closed-circuit television) in crash reconstruction, and directions in which software should be improved. The following results are useful for collision experts.

BASIN CONFIGURATION OF A SIX-DIMENSIONAL MODEL OF AN ELECTRIC POWER SYSTEM

2002 ◽  
Vol 12 (06) ◽  
pp. 1333-1356 ◽  
Author(s):  
YOSHISUKE UEDA ◽  
HIROYUKI AMANO ◽  
RALPH H. ABRAHAM ◽  
H. BRUCE STEWART
Keyword(s):  
Power Systems ◽  
Power System ◽  
Initial Conditions ◽  
Electrical Power ◽  
Practical Importance ◽  
Intervention Strategy ◽  
Basins Of Attraction ◽  
Electric Power System ◽  
Point Of View ◽  
Electrical Power System

As part of an ongoing project on the stability of massively complex electrical power systems, we discuss the global geometric structure of contacts among the basins of attraction of a six-dimensional dynamical system. This system represents a simple model of an electrical power system involving three machines and an infinite bus. Apart from the possible occurrence of attractors representing pathological states, the contacts between the basins have a practical importance, from the point of view of the operation of a real electrical power system. With the aid of a global map of basins, one could hope to design an intervention strategy to boot the power system back into its normal state. Our method involves taking two-dimensional sections of the six-dimensional state space, and then determining the basins directly by numerical simulation from a dense grid of initial conditions. The relations among all the basins are given for a specific numerical example, that is, choosing particular values for the parameters in our model.

3D Printing — The Basins of Tristability in the Lorenz System

2017 ◽  
Vol 27 (08) ◽  
pp. 1750128 ◽  
Author(s):  
Anda Xiong ◽  
Julien C. Sprott ◽  
Jingxuan Lyu ◽  
Xilu Wang
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Symmetric Pair ◽  
State Space Approach ◽  
3D Printers ◽  
The Lorenz System ◽  
Almost All ◽  
Space Approach

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

scholarly journals Stellar mass spectrum within massive collapsing clumps

2018 ◽  
Vol 611 ◽  
pp. A89 ◽  
Author(s):  
Yueh-Ning Lee ◽  
Patrick Hennebelle
Keyword(s):  
Large Scale ◽  
Equations Of State ◽  
Initial Conditions ◽  
Peak Position ◽  
Density Fluctuations ◽  
Initial Mass Function ◽  
Analytical Models ◽  
Numerical Resolution ◽  
Tidal Forces ◽  
The Imf

Context. Understanding the origin of the initial mass function (IMF) of stars is a major problem for the star formation process and beyond. Aim. We investigate the dependence of the peak of the IMF on the physics of the so-called first Larson core, which corresponds to the point where the dust becomes opaque to its own radiation. Methods. We performed numerical simulations of collapsing clouds of 1000 M⊙ for various gas equations of state (eos), paying great attention to the numerical resolution and convergence. The initial conditions of these numerical experiments are varied in the companion paper. We also develop analytical models that we compare to our numerical results. Results. When an isothermal eos is used, we show that the peak of the IMF shifts to lower masses with improved numerical resolution. When an adiabatic eos is employed, numerical convergence is obtained. The peak position varies with the eos, and using an analytical model to infer the mass of the first Larson core, we find that the peak position is about ten times its value. By analyzing the stability of nonlinear density fluctuations in the vicinity of a point mass and then summing over a reasonable density distribution, we find that tidal forces exert a strong stabilizing effect and likely lead to a preferential mass several times higher than that of the first Larson core. Conclusions. We propose that in a sufficiently massive and cold cloud, the peak of the IMF is determined by the thermodynamics of the high-density adiabatic gas as well as the stabilizing influence of tidal forces. The resulting characteristic mass is about ten times the mass of the first Larson core, which altogether leads to a few tenths of solar masses. Since these processes are not related to the large-scale physical conditions and to the environment, our results suggest a possible explanation for the apparent universality of the peak of the IMF.

scholarly journals Effect of Nonlinear Dissipation on the Basin Boundaries of a Driven Two-Well Modified Rayleigh–Duffing Oscillator

2015 ◽  
Vol 25 (02) ◽  
pp. 1550024 ◽  
Author(s):  
C. H. Miwadinou ◽  
A. V. Monwanou ◽  
J. B. Chabi Orou
Keyword(s):  
Initial Conditions ◽  
Duffing Oscillator ◽  
Excitation Amplitude ◽  
Nonlinear Damping ◽  
Homoclinic Bifurcation ◽  
Nonlinear Dissipation ◽  
Transition To Chaos ◽  
Melnikov Criterion ◽  
Quadratic Nonlinearities ◽  
Basin Boundaries

This paper considers the effect of nonlinear dissipation on the basin boundaries of a driven two-well modified Rayleigh–Duffing oscillator where pure cubic, unpure cubic, pure quadratic and unpure quadratic nonlinearities are considered. By analyzing the potential, an analytic expression is found for the homoclinic orbit. The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos. Unpure quadratic parameter and parametric excitation amplitude effects are found on the critical Melnikov amplitude μ cr . Finally, the phase space of initial conditions is carefully examined in order to analyze the effect of the nonlinear damping, and particularly how the basin boundaries become fractalized.

Stochastic Stability of a Universal-Joint Driven Torsional System

1999 ◽  
Author(s):  
S. F. Asokanthan ◽  
Xiao-Hui Wang
Keyword(s):  
Lyapunov Exponent ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Angular Speed ◽  
Analytical Models ◽  
Largest Lyapunov Exponent ◽  
Deterministic Case ◽  
Speed Fluctuation ◽  
The Difference ◽  
The Stability

Abstract Torsional instabilities in a two-degree-of-freedom system driven by a Hooke’s joint due to random input angular speed fluctuation are investigated. Linearised analytical models are used for calculating the largest Lyapunov exponent. Instability behaviour is then characterised by examining the sign of this exponent. Conditions for the onset of instability via sub-harmonic parametric resonances has been shown to coincide with those for the deterministic case. However, the onset of instability via sum as well as the difference type combination resonance is found to be different from that of the deterministic case. The instability conditions for the system under input angular speed fluctuation have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. Predictions for the deterministic and the stochastic cases are compared. The effect of fluctuation probability density as well as that of inertia loads on the stability behaviour of the system has been examined.

scholarly journals Soil nutrient cycles as a nonlinear dynamical system

2004 ◽  
Vol 11 (5/6) ◽  
pp. 589-598 ◽  
Author(s):  
S. Manzoni ◽  
A. Porporato ◽  
P. D'Odorico ◽  
F. Laio ◽  
I. Rodriguez-Iturbe
Keyword(s):  
Dynamical System ◽  
Initial Conditions ◽  
Nonlinear Dynamical System ◽  
Soil Nutrient ◽  
Steady State Solution ◽  
Basins Of Attraction ◽  
Climatic Conditions ◽  
Stable Node ◽  
Nutrient Cycles ◽  
Stable Focus

Abstract. An analytical model for the soil carbon and nitrogen cycles is studied from the dynamical system point of view. Its main nonlinearities and feedbacks are analyzed by considering the steady state solution under deterministic hydro-climatic conditions. It is shown that, changing hydro-climatic conditions, the system undergoes dynamical bifurcations, shifting from a stable focus to a stable node and back to a stable focus when going from dry, to well-watered, and then to saturated conditions, respectively. An alternative degenerate solution is also found in cases when the system can not sustain decomposition under steady external conditions. Different basins of attraction for "normal" and "degenerate" solutions are investigated as a function of the system initial conditions. Although preliminary and limited to the specific form of the model, the present analysis points out the importance of nonlinear dynamics in the soil nutrient cycles and their possible complex response to hydro-climatic forcing.

A Study of Noise Impact on the Stability of Electrostatic MEMS

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Yan Qiao ◽  
Wei Xu ◽  
Hongxia Zhang ◽  
Qin Guo ◽  
Eihab Abdel-Rahman
Keyword(s):  
Noise Intensity ◽  
Initial Conditions ◽  
Basins Of Attraction ◽  
Low Noise ◽  
Intensity Level ◽  
Lumped Mass ◽  
Mass Model ◽  
Restoring Force ◽  
Electrostatic Mems ◽  
The Stability

Abstract Noise-induced motions are a significant source of uncertainty in the response of micro-electromechanical systems (MEMS). This is particularly the case for electrostatic MEMS where electrical and mechanical sources contribute to noise and can result in sudden and drastic loss of stability. This paper investigates the effects of noise processes on the stability of electrostatic MEMS via a lumped-mass model that accounts for uncertainty in mass, mechanical restoring force, bias voltage, and AC voltage amplitude. We evaluated the stationary probability density function (PDF) of the resonator response and its basins of attraction in the presence noise and compared them to that those obtained under deterministic excitations only. We found that the presence of noise was most significant in the vicinity of resonance. Even low noise intensity levels caused stochastic jumps between co-existing orbits away from bifurcation points. Moderate noise intensity levels were found to destroy the basins of attraction of the larger orbits. Higher noise intensity levels were found to destroy the basins of attraction of smaller orbits, dominate the dynamic response, and occasionally lead to pull-in. The probabilities of pull-in of the resonator under different noise intensity level are calculated, which are sensitive to the initial conditions.

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