Analysis of grazing bifurcation from periodic motion to quasi-periodic motion in impact-damper systems

2016 ◽  
Vol 83 ◽  
pp. 112-118 ◽  
Author(s):  
Guilin Wen ◽  
Shan Yin ◽  
Huidong Xu ◽  
Sijin Zhang ◽  
Zengyao Lv
Keyword(s):  
Periodic Motion ◽  
Grazing Bifurcation ◽  
Impact Damper

Arbitrary Periodic Motions and Grazing Switching of a Forced Piecewise Linear, Impacting Oscillator

2006 ◽  
Vol 129 (3) ◽  
pp. 276-284 ◽  
Author(s):  
Albert C. J. Luo ◽  
Lidi Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Periodic Motion ◽  
Local Stability ◽  
Piecewise Linear ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Grazing Bifurcation ◽  
Piecewise Linear System ◽  
Local Stability Analysis ◽  
Mapping Structures

The grazing bifurcation and periodic motion switching of the harmonically forced, piecewise linear system with impacting are investigated. The generic mappings relative to the discontinuous boundaries of this piecewise system are introduced. Based on such mappings, the corresponding grazing conditions are obtained. The mapping structures are developed for the analytical prediction of periodic motions in such a system. The local stability and bifurcation conditions for specified periodic motions are obtained. The regular and grazing, periodic motions are illustrated. The grazing is the origin of the periodic motion switching for this system. Such a grazing bifurcation cannot be estimated through the local stability analysis. This model is applicable to prediction of periodic motions in nonlinear dynamics of gear transmission systems.

Grazing Bifurcation and Periodic Motion Switching in a Piecewise Linear, Impacting Oscillator Under a Periodical Excitation

2005 ◽  
Author(s):  
Albert C. J. Luo ◽  
Lidi Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Periodic Motion ◽  
Local Stability ◽  
Piecewise Linear ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Grazing Bifurcation ◽  
Piecewise Linear System ◽  
Local Stability Analysis ◽  
Mapping Structures

The grazing bifurcation and periodic motion switching of the harmonically forced, piecewise linear system with impacting are investigated. The generic mappings based on the discontinuous boundaries are introduced. Furthermore, the mapping structures are developed for the analytical prediction of periodic motions in such a system. The local stability and bifurcation conditions for specified periodic motions are obtained. The regular and grazing, periodic motions are illustrated. The grazing is the origin of the periodic motion switching for this system. Such a grazing bifurcation cannot be estimated through the local stability analysis. This model is applicable to prediction of periodic motions in nonlinear dynamics of gear transmission systems.

Stability and Bifurcation for the Equispaced, Periodic Motion of a Horizontal Impact Damper

2001 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Periodic Motion ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Periodic Excitation ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Impact Damper ◽  
Stability And Bifurcation ◽  
Period 2 ◽  
Good Agreement

Abstract Stability and bifurcation conditions for the asymmetric, periodic motion of a horizontal impact damper under a periodic excitation are developed through four mappings for two switch-planes relative to discontinuities. Period-doubling bifurcation for equispaced motion does not occur, but the asymmetric period-1 motions change to the asymmetric, period-2 ones through a period doubling bifurcation. A numerical prediction for equispaced to chaotic motions is completed. The numerical and analytical predictions of the periodic motion are in very good agreement. The asymmetric, periodic motions are also simulated.

Instability phenomena in impact damper system: From quasi-periodic motion to period-three motion

2017 ◽  
Vol 391 ◽  
pp. 170-179 ◽  
Author(s):  
Shan Yin ◽  
Guilin Wen ◽  
Yongkang Shen ◽  
Huidong Xu
Keyword(s):  
Periodic Motion ◽  
Impact Damper

scholarly journals Noise Reduction of Learning Control for Periodic Motion of Galvanometer Scanner

2020 ◽  
Vol 53 (2) ◽  
pp. 8401-8406
Author(s):  
Shingo Ito ◽  
Han Woong Yoo ◽  
Georg Schitter
Keyword(s):  
Noise Reduction ◽  
Periodic Motion ◽  
Learning Control ◽  
Galvanometer Scanner

scholarly journals Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Thomas Eiter ◽  
Mads Kyed
Keyword(s):  
Rigid Body ◽  
Sobolev Spaces ◽  
Periodic Motion ◽  
Viscous Incompressible Fluid ◽  
Body Motion ◽  
Translational Velocity ◽  
Ill Posed ◽  
Homogeneous Sobolev Spaces ◽  
The Mean ◽  
Time Periodic

AbstractThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

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