The Dynamics Research For An Autoparametric Dynamic Vibration Absorber

The autoparameter dynamic vibration absorber which is used by the transfer of energy to achieve damping vibration is a new type vibration-absorbing and shock absorbing device with rich dynamics properties.And the research of its dynamic properties also has great practical significance in the aspect of vibration damping. Based on the nonlinear dynamics and nonlinear vibration theory and method, complex dynamic behavior and chaotic vibration control of the autoparameter dynamic vibration absorber system is studied from the theoretical and numerical aspects. Main content of this paper are as follows:1. Summarized the research status, purposes and meaning of dynamic vibration absorber system, described some theoretical concepts and definitions,such as autoparameter vibration system,the multiple scale method,chaos, etc.,and made the brief summary and description to the main characteristic and analysis method of chaos,as well as chaotic vibration control.2. According to the Lagrange equation and Newton’s second law to establish the differential equation of autoparameter dynamic vibration absorber system. Using the multiple scale method to look for the second order approximate solution, and discuss its equilibrium solution. In the process of using the multiple scale method, we got two types of equilibrium solutions which are single mode and coupling mode.And the numerical simulation of the amplitude frequency response curve of this system is obtained. By the multiple scale method, the nonautonomous equations of original system can be converted into a new self-governing equations, its stability does not change, and we can use Routh-Hurwitz criterion for the new autonomous differential equations to judge its stability condition.The global dynamical behavior of the autoparameter dynamic vibration absorber system is studied by the numerical analysis method,and the existence of chaos is confirmed. Discussed the Situation when excitation frequency and amplitude respectively changed, obtained the chaotic region which is the autoparameter dynamic vibration absorber system produced. Analyzed its evolution process from periodic motion to chaos motion and found in the evolutionary process will be accompanied by Hopf bifurcation occurs.3. To the chaotic vibration control of autoparameter dynamic vibration absorber system. First of all, by changing nonlinear oscillator stiffness of the autoparameters dynamic vibration absorber system to realize the passive vibration control,and we can see the chaotic region decreases until it disappeared. Nonlinear spring of oscillator determines stiffness of the system, in other words, changing the spring materials of system (mainly stiffness change) is likely to achieve its chaos control.From the numerical analysis can be seen, if the stiffness values select properly, its chaos area can disappear, and chaotic vibration can be controlled. We can also see, if necessary the chaos area can be transferred to another new location by the stiffness selection.Then chaotic feedback control method is adopted to design feedback controller for the system, so as to realize chaotic control.Analysis dynamics characteristics to the after-controlled system.According maximum Lyapunov index which changes by the changed control parameters to select control value. From the phase diagram,we can see the chaotic motion is effectively controlled to the cycle track by the esigned feedback controller.4. Analysis and research a kind of multi-degree of freedom autoparameter dynamic vibration absorber.Based on the autoparameter dynamic vibration absorber, a new multi-degree of freedom autoparameter dynamic vibration absorber is built by increasing the vibration absorbing device. Also according to the Lagrange equation and Newton’s second law to establish the motion differential equation. After around the system model, mainly exploring its dynamic behavior characteristics by the numerical analysis method.