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.

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.

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.

COMPLEX DYNAMICS OF BILINEAR OSCILLATOR CLOSE TO GRAZING

2010 ◽  
Vol 20 (11) ◽  
pp. 3801-3817 ◽  
Author(s):  
EKATERINA PAVLOVSKAIA ◽  
JAMES ING ◽  
MARIAN WIERCIGROCH ◽  
SOUMITRO BANERJEE
Keyword(s):  
Complex Dynamics ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Basins Of Attraction ◽  
Experimental Investigations ◽  
Unstable Periodic Orbits ◽  
Chaotic Oscillations ◽  
Impact Oscillator ◽  
Parameter Values ◽  
Elastic Constraint

In this work the strange behavior of an impact oscillator with a one-sided elastic constraint discovered experimentally is compared with the predictions obtained using its mathematical model. Extensive experimental investigations undertaken on the rig developed at the Aberdeen University reveal different bifurcation scenarios under varying excitation frequency near grazing which were recorded for a number of values of the excitation amplitude. In the paper, particular attention is paid to the chaotic oscillations recorded near grazing frequency when a nonimpacting orbit becomes an impacting one under increasing excitation frequency. It was found that the evolution of the attractor is governed by a complex interplay between smooth and nonsmooth bifurcations, and the interactions between a number of coexisting orbits. The occurrence of coexisting attractors is manifested in the experimental results through discontinuous transitions from one orbit to another via boundary crisis. In some cases, the basins of attraction have a fractal structure. Detailed numerical exploration also revealed coexisting unstable periodic orbits. These stable and unstable coexisting orbits are often born far from the parameter values at which they influence the system dynamics. The very rich dynamics of the bilinear oscillator close to grazing is demonstrated and typical mechanisms of the attractors' appearance and disappearance are explained using stability analysis.

Efficacy of a Sliding Beam as a Nonlinear Vibration Isolator

2007 ◽  
Author(s):  
R. A. Ibrahim ◽  
R. J. Somnay
Keyword(s):  
Friction Coefficient ◽  
Initial Conditions ◽  
Excitation Frequency ◽  
Random Excitation ◽  
Excitation Power ◽  
Basins Of Attraction ◽  
System Response ◽  
Density Level ◽  
Vibration Isolator ◽  
Power Spectral

The influence of friction due to beam sliding at its supports on its dynamic behavior and its efficacy as a nonlinear isolator is studied numerically under sinusoidal and random excitation excitations. Under sinusoidal excitation, the equation of motion of the system is solved numerically and the solution is utilized to estimate the system transmissibility. It is found that when the excitation frequency is increased beyond resonance, the friction at the sliding supports serves to improve the transmissibility. The dependence of the response on initial conditions establishes the basins of attraction for different values of friction coefficient and excitation frequency and amplitude. Under random excitation, the system response statistics are estimated from Monte Carlo simulation results for different values of friction coefficient and excitation power spectral density level. The friction is found to result in a significant reduction of the system response mean square.

Intrinsic Localized Modes of Harmonic Oscillations in Nonlinear Oscillator Arrays

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Keisuke Nishimura
Keyword(s):  
Frequency Response ◽  
Initial Conditions ◽  
Excitation Frequency ◽  
Basins Of Attraction ◽  
Localized Modes ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Intrinsic Localized Modes ◽  
Mdof Systems ◽  
Oscillator Arrays

Intrinsic localized modes (ILMs) are investigated in an array with N Duffing oscillators that are weakly coupled with each other when each oscillator is subjected to sinusoidal excitation. The purpose of this study is to investigate the behavior of ILMs in nonlinear multi-degree-of-freedom (MDOF) systems. In the theoretical analysis, van der Pol's method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves are shown for N = 2 and 3 and compared with the results of the numerical simulations. Basins of attraction are shown for a two-oscillator array with hard-type nonlinearities to examine the possibility of appearance of ILMs when an oscillator is disturbed. The influences of the connecting springs for both hard- and soft-type nonlinearities on the appearance of the ILMs are examined. Increasing the values of the connecting spring constants may cause Hopf bifurcation followed by amplitude modulated motion (AMM) including chaotic vibrations. The influence of the imperfection of an oscillator is also investigated. Bifurcation sets are calculated to show the influence of the system parameters on the excitation frequency range of ILMs. Furthermore, time histories are shown for the case of N = 10, and many patterns of ILMs may appear depending on the initial conditions.

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.

Effects of Acoustic Excitation on a Swirling Diffusion Flame

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Michael E. Loretero ◽  
Rong F. Huang
Keyword(s):  
Flow Field ◽  
Bluff Body ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Mie Scattering ◽  
Flame Length ◽  
Laser Doppler Velocimeter ◽  
Scattering Method ◽  
Acoustic Excitation ◽  
Characteristic Modes

A swirling double concentric jet is commonly used for nonpremixed gas burner application for safety reasons and to improve the combustion performance. Fuel is generally spurted at the central jet while the annular coflowing air is swirled. They are normally separated by a blockage disk where the bluff-body effects further enhance the recirculation of hot gas at the reaction zone. This paper aims to experimentally investigate the behavior of flame and flow in a double concentric jet combustor when the fuel supply is acoustically driven. Laser-light sheet assisted Mie scattering method has been used to visualize the flow, while the flame lengths were measured by a conventional photography technique. The fluctuating velocity at the jet exit was measured by a two-component laser Doppler velocimeter. Flammability and stability at first fuel tube resonant frequency are reported and discussed. The evolution of flame profile with excitation level is presented and discussed, together with the reduction in flame length. The flame in the unforced reacting axisymmetric wake is classified into three characteristic modes, which are weak swirling flame, lifted flame, and transitional reattached flame. These terms reflect their primary features of flame appearances, and when the acoustic excitation is applied, the flame behaviors change with the excitation frequency and amplitude. Four additional characteristic modes are identified; e.g., at low excitation amplitudes, wrinkling flame with a blue annular film is observed because the excitation induces vortices in the central fuel jet and hence gives rise to the wrinkling of flame. The central jet vortices become larger with the increase in excitation amplitude and thus lead to a wider and shorter flame. If the excitation amplitude is increased above a certain value, the central jet vortices change the rotation direction and pacing with the annular jet vortices. These changes in the flow field induce large turbulent intensity and mixing and therefore make the flame looks blue and short. Further increase in the excitation amplitude would lift the flame because the flow field would be dramatically modified.

Modeling and Experimental Validations of a Piezoelectric Energy Harvester Under Combined Galloping and Base Excitations

2014 ◽  
Author(s):  
Amin Bibo ◽  
Abdessattar Abdelkefi ◽  
Mohammed F. Daqaq
Keyword(s):  
Bluff Body ◽  
Energy Harvester ◽  
Constitutive Relations ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Beam Theory ◽  
Excitation Amplitude ◽  
The Body ◽  
Base Excitation ◽  
Piezoelectric Energy

This paper develops an experimentally validated model of a piezoelectric energy harvester under combined aeroelastic-galloping and base excitations. To that end, an energy harvester consisting of a thin piezoelectric cantilever beam subjected to vibratory base excitation is considered. To permit galloping excitation, a bluff body is rigidly attached at the free end such that a net aerodynamic lift is generated as the incoming airflow separates on both sides of the body giving rise to limit cycle oscillations when the flow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitation is derived using the energy approach and by adopting the nonlinear Euler-Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The partial differential equations of the system are discretized and a reduced-order-model is obtained. The mathematical model is validated by conducting a series of experiments with different loading conditions represented by wind speed, base excitation amplitude, and excitation frequency around the primary resonance.

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.

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