Research of the periodic motion and stability of two-degree-of-freedom nonlinear oscillating systems

2002 ◽  
Vol 23 (10) ◽  
pp. 1229-1236 ◽  
Author(s):  
Liu Jun
Keyword(s):  
Periodic Motion ◽  
Degree Of Freedom ◽  
Oscillating Systems ◽  
Two Degree Of Freedom

Analytical Stability Improvement of the Periodic Vibro-Impact Processes

1999 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Krzysztof Tomczak
Keyword(s):  
Periodic Orbits ◽  
Periodic Motion ◽  
Feedback Loop ◽  
Degree Of Freedom ◽  
Loop Control ◽  
Analytical Stability ◽  
Impact Processes ◽  
Delay Loop ◽  
Sufficient Stability ◽  
Two Degree Of Freedom

Abstract In this paper an attention is focused on stabilisation improvement of periodic orbits of a one- and two-degree-of-freedom nonautonomous vibro-impact systems. This approach, among others, includes two problems. 1. A possibility of a sufficient stability improvement of the considered vibro-impact periodic motion using a feedback loop control is presented. 2. An original analytical averaging technique applied to a one-degree-of-freedom system is demonstrated. It enables to predict the efficient delay loop coefficients in order to achieve the desired stabilisation. In addition, an efficient delay loop control applied to two-degree-of-freedom system is proposed and illustrated.

Neimark-Sacker Bifurcations Near Degenerate Grazing Point in a Two Degree-of-Freedom Impact Oscillator

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Shan Yin ◽  
Jinchen Ji ◽  
Shuning Deng ◽  
Guilin Wen
Keyword(s):  
Periodic Motion ◽  
Small Neighborhood ◽  
Period Doubling ◽  
Degree Of Freedom ◽  
Grazing Impact ◽  
Mapping Technique ◽  
Impact Oscillator ◽  
Parameter Continuation ◽  
The Impact ◽  
Two Degree Of Freedom

Saddle-node or period-doubling bifurcations of the near-grazing impact periodic motions have been extensively studied in the impact oscillators, but the near-grazing Neimark-Sacker bifurcations have not been discussed yet. For the first time, this paper uncovers the novel dynamic behavior of Neimark-Sacker bifurcations, which can appear in a small neighborhood of the degenerate grazing point in a two degree-of-freedom impact oscillator. The higher order discontinuity mapping technique is used to determine the degenerate grazing point. Then, shooting method is applied to obtain the one-parameter continuation of the elementary impact periodic motion near degenerate grazing point and the peculiar phenomena of Neimark-Sacker bifurcations are revealed consequently. A two-parameter continuation is presented to illustrate the relationship between the observed Neimark-Sacker bifurcations and degenerate grazing point. New features that differ from the reported situations in literature can be found. Finally, the observed Neimark-Sacker bifurcation is verified by checking the existence and stability conditions in line with the generic theory of Neimark-Sacker bifurcation. The unstable bifurcating quasi-periodic motion is numerically demonstrated on the Poincaré section.

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