scholarly journals The Analysis of Grazing Periodic Motions in a Single Degree of Freedom Vibro-Impact System with Double Constrains

2015 ◽  
Vol 05 (04) ◽  
pp. 121-128
Author(s):  
洁琼 徐
Keyword(s):  
Degree Of Freedom ◽  
Periodic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impact System

Periodic Motions in a Single-Degree-of-Freedom System Under Both an Aerodynamic Force and a Harmonic Excitation

2019 ◽  
Author(s):  
Bo Yu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Aerodynamic Force ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Period

Abstract In this paper, a semi-analytical approach was used to predict periodic motions in a single-degree-of-freedom system under both aerodynamic force and harmonic excitation. Using the implicit mappings, the predictions of period-1 motions varying with excitation frequency are obtained. Stability of the period-1 motions are discussed, and the corresponding eigenvalues of period-1 motions are presented. Finally, numerical simulations of stable period-1 motions are illustrated.

Feedback Control of Grazing-Induced Chaos in the Single-Degree-of-Freedom Impact Oscillator

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Yongkang Shen ◽  
Shan Yin ◽  
Guilin Wen ◽  
Huidong Xu
Keyword(s):  
Feedback Control ◽  
Control Strategy ◽  
Dynamical Property ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Impact Oscillator ◽  
Continuous Transition ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Existence And Stability

Based on the special dynamical property of continuous transition at certain degenerate grazing points in the single-degree-of-freedom impact oscillator, the control problem of the grazing-induced chaos is investigated in this paper. To design degenerate grazing bifurcations, we show how to obtain the degenerate grazing points of the 1/n impact periodic motions by the existence and stability analysis first. Then, a discrete-in-time feedback control strategy is used to suppress the grazing-induced chaos into the 1/n impact periodic motions precisely by the desired degenerate grazing bifurcation. The feasibility of the control strategy is verified by numerical simulations.

scholarly journals External Periodic Force Control of a Single-Degree-of-Freedom Vibroimpact System

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jingyue Wang ◽  
Haotian Wang ◽  
Tie Wang
Keyword(s):  
Periodic Orbits ◽  
Force Control ◽  
Time History ◽  
Degree Of Freedom ◽  
Bifurcation And Chaos ◽  
Periodic Force ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impact System

A single-degree-of-freedom mechanical model of vibro-impact system is established. Bifurcation and chaos in the system are revealed with the time history diagram, phase trajectory map, and Poincaré map. According to the bifurcation and chaos of the actual vibro-impact system, the paper puts forward external periodic force control strategy. The method of controlling chaos by external periodic force feedback controller is developed to guide chaotic motions towards regular motions. The stability of the control system is also analyzed especially by theory. By selecting appropriate feedback coefficients, the unstable periodic orbits of the original chaotic orbit can be stabilized to the stable periodic orbits. The effectiveness of this control method is verified by numerical simulation.

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