Chaos Control Of Vibro-Impact Systems With Two Rigid Stops

Chaotic phenomenon is very common in nonlinear systems, and it is highly unstable.The chaos may cause surface wear,high frequency noise,low efficiency or even equipment damage without controlling. So the research of chaos co.ntrol has importance and practical significance. The chaos control of the vibro-impact system with two rigid stops is investigated in this dissertation.The main aspects of the research are:(1)Implusive control method and newly proposed mixed control method in this dissertation,i.e., implusive-damping control method,are applied to suppress chaotic behavior to period-one or period-two orbit in the single-degree-of-freed-om vibro-impact system with two rigid stops.At first,the Poincare map of vibro-impact system with two rigid stops is constructed by local maps between different stages in whole motion process of the system. The spectrum of Lyapun-ov exponents of vibro-impact system with two rigid stops are computed using previously presented Poincare map.The Lyapunov exponent and the phase portrait are used to verify the existence of chaos of the system. Then,the chaos in the system is controlled by the two methods,respectively.The bifurcation diagr am,the phase portrait and the control effect diagram for the controlled system are obtained with numerical simulations.At last,the two control methods are compared from aspects of the control scope and the speed reaching the stable state after controlling.The result shows that mixed control method is better than implusive control method.(2)Implusive control method and periodical exciting force method are used to suppressing chaotic behavior to the period-two or period-three orbit in the two-degree-of-freedom vibro-impact system with two rigid stops.At first,the Lyapunov exponent of two-degree-of-freedom vibro-impact system with two rigid stops is calculated as the method used in the single-degree-of-freedom vibro-impact system with two rigid stops,and the chaos of the system is verified by Lyapunov exponent.Then,the chaos in the system is controlled through implusive control method and periodical exciting force method.The phase portrait and the control effect diagram for the controlled system are given by numerical simulations.At last,the results after controlling are analyzed and it shows that the two chaos control methods are valid for the two-degree-of-freed-om vibro-impact system with two rigid stops.