Complex Motions in Horizontal Impact Pairs With a Periodic Excitation

2011 ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Bifurcation Analysis ◽  
Periodic Motion ◽  
Analytical Prediction ◽  
Periodic Excitation ◽  
Chaotic Motions ◽  
Discontinuous Dynamical System ◽  
Stability And Bifurcation ◽  
Stability And Bifurcation Analysis

In this paper, the horizontal impact pair with a periodic excitation is studied from the theory of discontinuous dynamical system. Analytical conditions for motion switching are obtained. From generic mappings, analytical prediction of periodic motion is presented, and the corresponding stability and bifurcation analysis are carried out. Periodic and chaotic motions are illustrated numerically.

Analytical Predication of Complex Motion of a Ball in a Periodically Shaken Horizontal Impact Pair

2011 ◽  
Vol 7 (2) ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Bifurcation Analysis ◽  
Periodic Motion ◽  
Analytical Prediction ◽  
Periodic Excitation ◽  
Complex Motion ◽  
Chaotic Motions ◽  
Discontinuous Dynamical System ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis

In this paper, complex motions of a ball in the horizontal impact pair with a periodic excitation are studied analytically using the theory of discontinuous dynamical system. Analytical conditions for motion switching caused by impacts are developed, and generic mapping structures are introduced to describe different periodic and chaotic motions. Analytical prediction of complex periodic motion of the ball in the periodically shaken impact pair is completed, and the corresponding stability and bifurcation analysis are also carried out. Numerical illustrations of periodic and chaotic motions are given.

Periodic Motions in the Periodically Forced Oscillator With Multiple Discontinuities

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Mehul T. Patel
Keyword(s):  
Dynamical System ◽  
Bifurcation Analysis ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Forced Oscillator ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper, the stability and bifurcation of periodic motions in periodically forced oscillator with multiple discontinuities is investigated. The generic mappings are introduced for the analytical prediction of periodic motions. Owing to the multiple discontinuous boundaries, the mapping structures for periodic motions are very complicated, which causes more difficulty to obtain periodic motions in such a dynamical system. The analytical prediction of complex periodic motions is carried out and verified numerically, and the corresponding stability and bifurcation analysis are performed. Due to page limitation, grazing and stick motions and chaos in this system will be investigated further.

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.

SINGULARITY, SWITCHABILITY AND BIFURCATIONS IN A 2-DOF, PERIODICALLY FORCED, FRICTIONAL OSCILLATOR

2013 ◽  
Vol 23 (03) ◽  
pp. 1330009 ◽  
Author(s):  
ALBERT C. J. LUO ◽  
MOZHDEH S. FARAJI MOSADMAN
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Degrees Of Freedom ◽  
Eigenvalue Analysis ◽  
Analytical Dynamics ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper, the analytical dynamics for singularity, switchability, and bifurcations of a 2-DOF friction-induced oscillator is investigated. The analytical conditions of the domain flow switchability at the boundaries and edges are developed from the theory of discontinuous dynamical systems, and the switchability conditions of boundary flows from domain and edge flows are presented. From the singularity and switchability of flow to the boundary, grazing, sliding and edge bifurcations are obtained. For a better understanding of the motion complexity of such a frictional oscillator, switching sets and mappings are introduced, and mapping structures for periodic motions are adopted. Using an eigenvalue analysis, the stability and bifurcation analysis of periodic motions in the friction-induced system is carried out. Analytical predictions and parameter maps of periodic motions are performed. Illustrations of periodic motions and the analytical conditions are completed. The analytical conditions and methodology can be applied to the multi-degrees-of-freedom frictional oscillators in the same fashion.

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