Dynamics of an Electromechanical System With Angular and Ferroresonant Nonlinearities

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
D. O. Tcheutchoua Fossi ◽  
P. Woafo
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Harmonic Balance ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Electromechanical System ◽  
Bifurcation Diagrams ◽  
Oscillatory Solutions ◽  
Torsion Bar ◽  
Hysteresis Phenomena

The purpose of this paper is to study the dynamics of an electromechanical system consisting of a torsion-bar or two mechanical pumps activated by an electromotor. Oscillatory solutions showing the jump and hysteresis phenomena are obtained using the harmonic balance method and direct numerical simulation. Chaotic behavior is presented via the bifurcation diagrams and corresponding Lyapunov exponent. Some implications of the results on the applications of the devices are discussed.

Bifurcation Analysis of a Power System Model with Three Machines and Four Buses

2016 ◽  
Vol 26 (05) ◽  
pp. 1650082 ◽  
Author(s):  
Yu Chang ◽  
Xiaoli Wang ◽  
Dashun Xu
Keyword(s):  
Power Systems ◽  
Power System ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Period Doubling ◽  
Bifurcation Phenomena ◽  
Fold Bifurcation ◽  
Approximate Expressions

The bifurcation phenomena in a power system with three machines and four buses are investigated by applying bifurcation theory and harmonic balance method. The existence of saddle-node bifurcation and Hopf bifurcation is analyzed in time domain and in frequency domain, respectively. The approach of the fourth-order harmonic balance is then applied to derive the approximate expressions of periodic solutions bifurcated from Hopf bifurcations and predict their frequencies and amplitudes. Since the approach is valid only in some neighborhood of a bifurcation point, numerical simulations and the software Auto2007 are utilized to verify the predictions and further study bifurcations of these periodic solutions. It is shown that the power system may have various types of bifurcations, including period-doubling bifurcation, torus bifurcation, cyclic fold bifurcation, and complex dynamical behaviors, including quasi-periodic oscillations and chaotic behavior. These findings help to better understand the dynamics of the power system and may provide insight into the instability of power systems.

scholarly journals Harmonic Balance Method for Chaotic Dynamics in Fractional-Order Rössler Toroidal System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Huijian Zhu
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Harmonic Balance ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Chaotic Motions ◽  
Behavior Based

This paper deals with the problem of determining the conditions under which fractional order Rössler toroidal system can give rise to chaotic behavior. Based on the harmonic balance method, four detailed steps are presented for predicting the existence and the location of chaotic motions. Numerical simulations are performed to verify the theoretical analysis by straightforward computations.

Shilnikov Chaos and Dynamics of a Self-Sustained Electromechanical Transducer

2000 ◽  
Vol 123 (2) ◽  
pp. 170-174 ◽  
Author(s):  
J. C. Chedjou ◽  
P. Woafo ◽  
S. Domngang
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Critical Points ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
The Stability

The dynamics of a self-sustained electromechanical transducer is studied. The stability of the critical points is analyzed using the analytic Routh-Hurwitz criterion. Analytic oscillatory solutions are obtained in both the resonant and non-resonant cases. Chaotic behavior is observed using the Shilnikov theorem and from a direct numerical simulation of the equations of motion.

Dynamic vibratory motion analysis of a multi-degree-of-freedom torsional system with strongly stiff nonlinearities

2014 ◽  
Vol 229 (8) ◽  
pp. 1399-1414 ◽  
Author(s):  
Jong-yun Yoon ◽  
Hyeongill Lee
Keyword(s):  
Numerical Simulation ◽  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Nonlinear Frequency ◽  
Dynamic Behaviors ◽  
Resonance Frequencies ◽  
Torsional System

Physical driveline systems have inherent nonlinearities such as multiple piecewise linear springs, gear backlashes, and drag torques. The multi-staged clutch dampers, in particular, cause severe problems in simulating the nonlinear dynamic behaviors of multi-degree-of-freedom systems. In order to analyze the nonlinear dynamic behaviors of the system, the harmonic balance method has been employed. This study suggests a method to overcome the convergence problems with strong nonlinearities by employing two distinct smoothening factors for stiffness and hysteresis. First, the dynamic behaviors of the multi-degree-of-freedom torsional system are investigated by employing multi-staged clutch dampers subjected to a sinusoidal excitation. Second, the effects of system parameters are examined with respect to dynamic characteristics of torsional vibration. The regimes of resonance frequencies along with the relevant parameters of the system are investigated by calculating backbone curves, which reduce the calculation time significantly. In order to validate harmonic balance method simulation, the simulated results are compared with those of numerical simulation. Harmonic balance method is shown to be more efficient than numerical simulation in calculating the nonlinear frequency response, as well as in simulating the steady-state responses without transient response effect.

scholarly journals Dynamical properties of a novel one dimensional chaotic map

2022 ◽  
Vol 19 (3) ◽  
pp. 2489-2505
Author(s):  
Amit Kumar ◽  
◽  
Jehad Alzabut ◽  
Sudesh Kumari ◽  
Mamta Rani ◽  
...  
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Behavior ◽  
Chaotic Map ◽  
Logistic Map ◽  
Maximal Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
One Dimensional ◽  
Dynamical Properties ◽  
Chaotic Logistic Map

<abstract><p>In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu &gt; 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.</p></abstract>

Harmonic Balance Analysis for the Oscillations of Magnetic Levitation

2014 ◽  
Vol 672-674 ◽  
pp. 1554-1557
Author(s):  
Zu Yao Wang
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Frequency Response ◽  
Harmonic Balance ◽  
Magnetic Levitation ◽  
Harmonic Balance Method ◽  
Weakly Nonlinear ◽  
Amplitude Frequency Response ◽  
Strongly Nonlinear System ◽  
Balance Analysis

This paper investigates a design and analysis of a novel energy harvester that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equation of the system which could be derived based on the Newton’s second law is reduced to the form of a Duffing’s equation. The system steady-state amplitude frequency response relationship is analyzed by harmonic balance and numerical simulation, respectively. In the weakly nonlinear system, the curve of amplitude frequency response using harmonic balance method accords with the curve using numerical simulation;and in the strongly nonlinear system, the curve using harmonic balance basically accords with the curve using numerical simulation as well.

Numerical simulation of transonic compressor under circumferential inlet distortion and rotor/stator interference using harmonic balance method

2018 ◽  
Vol 32 (12n13) ◽  
pp. 1840021
Author(s):  
Ziwei Wang ◽  
Xiong Jiang ◽  
Ti Chen ◽  
Yan Hao ◽  
Min Qiu
Keyword(s):  
Numerical Simulation ◽  
Unsteady Flow ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Transonic Compressor ◽  
Inlet Distortion ◽  
Speed Up ◽  
Computational Resources ◽  
Optimizing Algorithm

Simulating the unsteady flow of compressor under circumferential inlet distortion and rotor/stator interference would need full-annulus grid with a dual time method. This process is time consuming and needs a large amount of computational resources. Harmonic balance method simulates the unsteady flow in compressor on single passage grid with a series of steady simulations. This will largely increase the computational efficiency in comparison with the dual time method. However, most simulations with harmonic balance method are conducted on the flow under either circumferential inlet distortion or rotor/stator interference. Based on an in-house CFD code, the harmonic balance method is applied in the simulation of flow in the NASA Stage 35 under both circumferential inlet distortion and rotor/stator interference. As the unsteady flow is influenced by two different unsteady disturbances, it leads to the computational instability. The instability can be avoided by coupling the harmonic balance method with an optimizing algorithm. The computational result of harmonic balance method is compared with the result of full-annulus simulation. It denotes that, the harmonic balance method simulates the flow under circumferential inlet distortion and rotor/stator interference as precise as the full-annulus simulation with a speed-up of about 8 times.

Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

2015 ◽  
Vol 5 (4) ◽  
Author(s):  
Athina Bougioukou
Keyword(s):  
Lyapunov Exponent ◽  
Stock Market ◽  
Chaos Theory ◽  
Linear Dependence ◽  
Chaotic Behavior ◽  
Efficient Market Hypothesis ◽  
Chaotic Behaviour ◽  
Maximum Lyapunov Exponent ◽  
Efficient Market ◽  
General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

scholarly journals Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 474 ◽  
Author(s):  
Lazaros Moysis ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jesus M. Munoz-Pacheco ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Image Encryption ◽  
Fuzzy Numbers ◽  
Statistical Tests ◽  
Logistic Map ◽  
Simple Rule ◽  
Pseudorandom Number ◽  
Bifurcation Diagrams ◽  
Triangular Numbers ◽  
Pseudorandom Number Generation

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

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