Chaos Control In Rub-Impact Rotor Mapping Systems

Chaos,an important nonlinear phenomenon,is a kind of unpredictable motion because of the nonlinear system's sensitivity to initial conditions.Nonlinear factors in systems make their dynamics very complex,always leading to chaos,not random.In most cases,chaos is anticipated to be controlled into regular motion or be eventually eliminated in kinds of related engineering.Therefore,research of controlling chaos techniques and their applications has begun to take a big place in natural science and technology in the past tens of years.As far as we are concerned,there are also many devastating chaotic motions in rotary machines,which needs more attentions. In this paper,the main content includes theoretical and numerical studies on controling chaos with nonlinear feedback method,and its application in rotor systems.It is listed in details as follows:1. A nonlinear feedback method to control chaos into regular motions is introduced in details with its merits; A two-dimensional smooth mapping system can be controlled from chaos to a stable period-2 orbit by the nonlinear feedback chaos control method.2.The stability problem of the grazing period-1 motion can be discussed by the stability theory;Through numerical iteration the typical grazing bifurcations are found,with different size of chaos band referred to certain parameter.3. The nonlinear feedback chaos control method is adopted for the four-dimensional piecewise-smooth rub-impact rotor mapping systems.The rub-impact motions are stabilized into the impact period-1 motion or single impact period-2 motion by choosing the gain of control properly,and further development of chaos can thus be successfully avoided, additionally with some results of numerical simulation. The rub-impact motions can also be stablized into the grazing period-1 motion by using the control method.