scholarly journals Bifurcation and chaos in some relative rotation systems with Mathieu-Duffing oscillator

2013 ◽  
Vol 62 (23) ◽  
pp. 234501
Author(s):  
Hou Dong-Xiao ◽  
Zhao Hong-Xu ◽  
Liu Bin
Keyword(s):  
Duffing Oscillator ◽  
Relative Rotation ◽  
Bifurcation And Chaos

scholarly journals Bifurcation and chaos of some strongly nonlinear relative rotation system with time-varying clearance

2014 ◽  
Vol 63 (7) ◽  
pp. 074501
Author(s):  
Liu Bin ◽  
Zhao Hong-Xu ◽  
Hou Dong-Xiao ◽  
Liu Hao-Ran
Keyword(s):  
Time Varying ◽  
Relative Rotation ◽  
Bifurcation And Chaos ◽  
Strongly Nonlinear ◽  
Rotation System

scholarly journals Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Yu Zhang ◽  
Longsuo Li
Keyword(s):  
Chaotic Behavior ◽  
Duffing Oscillator ◽  
Dynamical Behavior ◽  
Gaussian White Noise ◽  
Stable State ◽  
Phase Portraits ◽  
Relative Rotation ◽  
Chaos Analysis ◽  
Rotation System ◽  
And Control

Chaos analysis and control of relative rotation nonlinear dynamic system with Mathieu-Duffing oscillator are investigated. By using Lagrange equation, the dynamics equation of relative rotation system has been established. Melnikov’s method is applied to predict the chaotic behavior of this system. Moreover, the chaotic dynamical behavior can be controlled by adding the Gaussian white noise to the proposed system for the sake of changing chaos state into stable state. Through numerical calculation, the Poincaré map analysis and phase portraits are carried out to confirm main results.

Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system

2014 ◽  
Vol 23 (9) ◽  
pp. 094501 ◽  
Author(s):  
Shuang Liu ◽  
Shuang-Shuang Zhao ◽  
Bao-Ping Sun ◽  
Wen-Ming Zhang
Keyword(s):  
Electromechanical Coupling ◽  
Relative Rotation ◽  
Bifurcation And Chaos ◽  
Chaos Analysis ◽  
Rotation System

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

Suppressing Chaos in a Nonideal Double-Well Oscillator Using an Based Electromechanical Damped Device

2014 ◽  
Vol 706 ◽  
pp. 25-34 ◽  
Author(s):  
G. Füsun Alişverişçi ◽  
Hüseyin Bayiroğlu ◽  
José Manoel Balthazar ◽  
Jorge Luiz Palacios Felix
Keyword(s):  
Numerical Simulations ◽  
Chaotic Dynamics ◽  
Duffing Oscillator ◽  
Vibration Energy ◽  
Vibration Absorber ◽  
Electrical System ◽  
Chaotic Vibration ◽  
System A ◽  
Ideal System ◽  
Double Well Potential

In this paper, we analyzed chaotic dynamics of an electromechanical damped Duffing oscillator coupled to a rotor. The electromechanical damped device or electromechanical vibration absorber consists of an electrical system coupled magnetically to a mechanical structure (represented by the Duffing oscillator), and that works by transferring the vibration energy of the mechanical system to the electrical system. A Duffing oscillator with double-well potential is considered. Numerical simulations results are presented to demonstrate the effectiveness of the electromechanical vibration absorber. Lyapunov exponents are numerically calculated to prove the occurrence of a chaotic vibration in the non-ideal system and the suppressing of chaotic vibration in the system using the electromechanical damped device.

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