scholarly journals Bifurcation and chaos of some relative rotation system with triple-well Mathieu-Duffing oscillator

2014 ◽  
Vol 63 (17) ◽  
pp. 174502
Author(s):  
Liu Bin ◽  
Zhao Hong-Xu ◽  
Hou Dong-Xiao
Keyword(s):  
Duffing Oscillator ◽  
Relative Rotation ◽  
Bifurcation And Chaos ◽  
Rotation System

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

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 The Nonsmooth Vibration of a Relative Rotation System with Backlash and Dry Friction

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Minjia He ◽  
Shuo Li ◽  
Jinjin Wang ◽  
Zhenjun Lin ◽  
Shuang Liu
Keyword(s):  
Dry Friction ◽  
Time History ◽  
Static Friction ◽  
Friction Torque ◽  
Relative Rotation ◽  
Rotation System ◽  
Inclusion Theory ◽  
Nonsmooth Dynamical Systems ◽  
Driving Torque ◽  
Function Time

We investigate a relative rotation system with backlash and dry friction. Firstly, the corresponding nonsmooth characters are discussed by the differential inclusion theory, and the analytic conditions for stick and nonstick motions are developed to understand the motion switching mechanism. Based on such analytic conditions of motion switching, the influence of the maximal static friction torque and the driving torque on the stick motion is studied. Moreover, the sliding time bifurcation diagrams, duty cycle figures, time history diagrams, and the K-function time history diagram are also presented, which confirm the analytic results. The methodology presented in this paper can be applied to predictions of motions in nonsmooth dynamical systems.

scholarly journals Chaos and the control of multi-time delay feedback for some nonlinear relative rotation system

2013 ◽  
Vol 62 (9) ◽  
pp. 094502
Author(s):  
Zhang Wen-Ming ◽  
Li Xue ◽  
Liu Shuang ◽  
Li Ya-Qian ◽  
Wang Bo-Hua
Keyword(s):  
Time Delay ◽  
Relative Rotation ◽  
Rotation System

Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic

2015 ◽  
Vol 24 (7) ◽  
pp. 074501 ◽  
Author(s):  
Shuang Liu ◽  
Zhao-Long Wang ◽  
Shuang-Shuang Zhao ◽  
Hai-Bin Li ◽  
Jian-Xiong Li
Keyword(s):  
Bifurcation Analysis ◽  
Relative Rotation ◽  
Grazing Bifurcation ◽  
Rotation System
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