Studies On New Mechanism Of Self-excited Vibration Suppression

Self-excited vibration widely exists in engineering, such as flutter of the foil,cutting vibration, galloping of electric power transmission line, vibration of flexiblemaking system etc. so it's a hot topic to depress and control the self-excited vibration,at the same time, it always relates to the hopf bifurcation of a system, so the control ofself-excited vibration tightly corresponds with the study of hot topics in nonlineardynamics, bifurcation control.In allusion to the most typical self-excited system, van der Pol oscillator, it bringsforward a new thinking that we couple it with a resonantly forced Duffing oscillatorby right of nonlinear damping, to reduce the vibration of it.First of all, this paper uses multiple scales to get the average equation, and theone-step closed bifurcation equations of double mode solution and single modesolution. it points out through analysis: the double mode solution bifurcationbelongs to double limits constrained bifurcation, we also use forced amplitude,frequency, and the nonlinear triple spring as bifurcation parameters, to get theconstrained bifurcation modes, the theory solution accords with the numeric solutionvery well. As of the single mode solution bifurcation, because of the shortage ofmultiple scales, we use IHB method to compute and analyze.Double mode solution bifurcation, singularity analysis and numericalcomputation show: with proper parameters, self-excited vibration can be suppressedvery well even to zero. When the forced amplitude f increased form small to large,main system's vibration fall step by step at first, and then lose stabilization, a vibrationwith the frequency same as the forced power appeared in its solution, then became thesingle mode movement. Its vibration pricked up as f arisen, so there is a prime valueof f.We discussed the depression of the flutter of airfoil as a primary application ofabove. Numerical analysis show: the duffing subsystem effect the upright vibration ofthe airfoil greatly, especially when Q is much larger;but has little effect on thevibration of elevation direction, only simplify its vibration. All these show that theprecept has some redeeming feature.Other parameters effect on the depression purpose in the typical self-excitedengineering vibration, need more consideration.We declared all above in the paper benefit the design of new self-excitedvibration depression oscillator.