ON AUTOPARAMETRIC ROUTE LEADING TO CHAOS IN DYNAMICAL SYSTEMS

2002 ◽  
Vol 12 (04) ◽  
pp. 819-826 ◽  
Author(s):  
S. N. VLADIMIROV ◽  
V. V. NEGRUL
Keyword(s):  
Numerical Simulation ◽  
Phase Space ◽  
Dynamical Systems ◽  
Equilibrium State ◽  
Dynamic Systems ◽  
Strange Attractor ◽  
Oscillatory Systems ◽  
Physical Experiments ◽  
Bifurcation Phenomena ◽  
Infinite Dimensionality

Features of transition from regular types of oscillations to chaos in dynamic systems with finite and infinite dimensionality of phase space have been discussed. It has been found that for some types of nonlinearity, transition to the chaotic motion in these systems occurs according to the identical autoparametric scenario. The sequence of bifurcation phenomena looks as follows: equilibrium state ⇒ limit cycle ⇒ semitorus ⇒ strange attractor. On the basis of the results of numerical simulation a conclusion was made about the typical nature of such a scenario. The results of numerical calculations are confirmed by results of physical experiments carried out on the base of radiophysical self-oscillatory systems.

A Methodology for the Modeling of Rail Vehicles From Time Series Measurements Using Time-Delay Neural Networks

2007 ◽  
Author(s):  
John Zolock ◽  
Robert Greif
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Dynamical Systems ◽  
Dynamic Systems ◽  
Phase Space Reconstruction ◽  
Series Data ◽  
Modeling Methodology ◽  
Forcing Function

The main goal of this research is to develop and demonstrate a general, efficient, mathematically and theoretically based methodology to model nonlinear forced vibrating mechanical systems from time series measurements. A system identification modeling methodology for forced dynamical systems is presented based on dynamic system theory and nonlinear time series analysis that employs phase space reconstruction (delay vector embedding) for modeling of dynamical systems from time series data using time-delay neural networks (TDNN). The first part of this work details the modeling methodology including background on dynamic systems, phase space reconstruction, and neural networks. In the second part of this work the methodology is evaluated based on its ability to model selected analytical lumped parameter forced vibrating dynamic systems including an example of a linear system predicting lumped mass displacement using a displacement forcing. function The work discusses the application to nonlinear systems, multi degree-of-freedom systems, and multi-input systems. The methodology is further evaluated on its ability to model an analytical passenger rail vehicle predicting vertical wheel/rail force using vertical rail profile as input. Studying the neural modeling methodology using an analytical systems shows the clearest observations from results which provide prospective users of this tool an understanding of the expectations and limitations of the modeling methodology.

A Methodology for the Modeling of Forced Dynamical Systems From Time Series Measurements Using Time-Delay Neural Networks

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
John Zolock ◽  
Robert Greif
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Dynamical Systems ◽  
Dynamic Systems ◽  
Phase Space Reconstruction ◽  
Series Data ◽  
Modeling Methodology ◽  
Forcing Function

The main goal of this research was to develop and present a general, efficient, mathematical, and theoretical based methodology to model nonlinear forced-vibrating mechanical systems from time series measurements. A system identification modeling methodology for forced dynamical systems is presented based on a dynamic system theory and a nonlinear time series analysis that employ phase space reconstruction (delay vector embedding) in modeling dynamical systems from time series data using time-delay neural networks. The first part of this work details the modeling methodology, including background on dynamic systems, phase space reconstruction, and neural networks. In the second part of this work, the methodology is evaluated based on its ability to model selected analytical lumped-parameter forced-vibrating dynamic systems, including an example of a linear system predicting lumped mass displacement subjected to a displacement forcing function. The work discusses the application to nonlinear systems, multiple degree of freedom systems, and multiple input systems. The methodology is further evaluated on its ability to model an analytical passenger rail car predicting vertical wheel∕rail force using a measured vertical rail profile as the input function. Studying the neural modeling methodology using analytical systems shows the clearest observations from results, providing prospective users of this tool an understanding of the expectations and limitations of the modeling methodology.

Harmonic Oscillators with Nonlinear Damping

2017 ◽  
Vol 27 (11) ◽  
pp. 1730037 ◽  
Author(s):  
J. C. Sprott ◽  
W. G. Hoover
Keyword(s):  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Strange Attractor ◽  
Nonlinear Damping ◽  
Harmonic Oscillators ◽  
Coexisting Attractors ◽  
Simple Harmonic Oscillator ◽  
Interesting Behavior

Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

Preliminary results of numerical simulation of submarine landslide-generated waves

2021 ◽  
Author(s):  
Ramtin Sabeti ◽  
Mohammad Heidarzadeh
Keyword(s):  
Numerical Simulation ◽  
Numerical Modelling ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Source Region ◽  
Three Dimensional ◽  
Terminal Velocity ◽  
Sensitivity Analyses ◽  
Physical Experiments ◽  
Set Up

<p>Landslide-generated waves have been major threats to coastal areas and have led to destruction and casualties. Their importance is undisputed, most recently demonstrated by the 2018 Anak Krakatau tsunami, causing several hundred fatalities. The accurate prediction of the maximum initial amplitude of landslide waves (<em>η<sub>max</sub></em>) around the source region is a vital hazard indicator for coastal impact assessment. Laboratory experiments, analytical solutions and numerical modelling are three major methods to investigate the (<em>η<sub>max</sub></em>). However, the numerical modelling approach provides a more flexible and cost- and time-efficient tool. This research presents a numerical simulation of tsunamis due to rigid landslides with consideration of submerged conditions. In particular, this simulation focuses on studying the effect of landslide parameters on <em>η<sub>max</sub>.</em> Results of simulations are compared with our conducted physical experiments at the Brunel University London (UK) to validate the numerical model.</p><p>We employ the fully three-dimensional computational fluid dynamics package, FLOW-3D Hydro for modelling the landslide-generated waves. This software benefit from the Volume of Fluid Method (VOF) as the numerical technique for tracking and locating the free surface. The geometry of the simulation is set up according to the wave tank of physical experiments (i.e. 0.26 m wide, 0.50 m deep and 4.0 m). In order to calibrate the simulation model based on the laboratory measurements, the friction coefficient between solid block and incline is changed to 0.41; likewise, the terminal velocity of the landslide is set to 0.87 m/s. Good agreement between the numerical solutions and the experimental results is found. Sensitivity analyses of landslide parameters (e.g. slide volume, water depth, etc.) on <em>η<sub>max </sub></em>are performed. Dimensionless parameters are employed to study the sensitivity of the initial landslide waves to various landslide parameters.</p>

scholarly journals Numerical Simulation and Experimental Study of Capacitive Imaging Technique as a Non-Destructive Testing Method

2021 ◽  
Author(s):  
Farima Abdollahi Mamoudan ◽  
Sebastien Savard ◽  
Tobin Filleter ◽  
Clemente Ibarra-Castanedo ◽  
Xavier Maldague
Keyword(s):  
Numerical Simulation ◽  
Surface Defects ◽  
Capacitive Sensor ◽  
Experimental Result ◽  
Destructive Testing ◽  
Fe Modelling ◽  
Inspection Method ◽  
Physical Experiments ◽  
Imaging Performance ◽  
Non Destructive

It was recently demonstrated that a co-planar capacitive sensor could be applied to the evaluation of materials without the disadvantages associated with the other techniques. This technique effectively detects changes in the dielectric properties of the materials due to, for instance, imperfections or variations in the internal structure, by moving a set of simple electrodes on the surface of the specimen. An AC voltage is applied to one or more electrodes and signals are detected by others. This is a promising inspection method for imaging the interior structure of the numerous materials, without the necessity to be in contact with the surface of the sample. In this paper, Finite Element (FE) modelling was employed to simulate the electric field distribution from a co-planar capacitive sensor and the way it interacts with a non-conducting sample. Physical experiments with a prototype capacitive sensor were also performed on a Plexiglas sample with sub-surface defects, to assess the imaging performance of the sensor. A good qualitative agreement was observed between the numerical simulation and experimental result.

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