分数阶时滞动力吸振器对主系统振动影响  

Fractional delay resonator and its effects on vibrations of primary systems

作　　者：宋洪涛[1] 沈玉凤[1] 荆栋[1] 刘灿昌[1] 

机构地区：[1]山东理工大学交通与车辆工程学院,山东淄博255049

出　　处：《广西大学学报（自然科学版）》2016年第2期388-394,共7页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(51275280)

摘　　要：为了研究分数阶时滞动力吸振器对主系统振动的影响,仿照整数阶导数的时滞动力吸振器的设计原理,提出了一种分数阶导数的时滞动力吸振器吸振理论。通过对高哲法的逆向推导,研究分数阶时滞动力吸振器的固有频率与反馈增益关系的确定方法,该方法可以在频率变化的情况下,允许分数阶时滞动力吸振器的固有频率实时跟踪外激励频率而变化。研究发现在保证主系统和动力吸振器稳定的情况下,在一定时滞范围内,通过增加动力吸振器的时滞量可以减小主系统的振动幅值。通过数据仿真分析证明了这种新方法确实可行,吸振器减振效果明显,振动源在加入新型动力吸振器后振动减少了99%左右,几乎将振动完全吸收;在被动型动力吸振器吸振效果降低时,新型的动力吸振器仍然能达到83%的吸振效果。In order to study the influence of fractional order delay dynamic vibration absorber on the vibration of the main system,a delay dynamic fractional derivative vibration absorbing theory was proposed following the design principle of delay dynamic integer order derivatives vibration absorber.The relationship between the natural frequency of the fractional delay dynamic vibration absorber and feedback gain was determined by reverse derivation of Gao-Zhe method. This method can be in variable occasions,real-time tracking of natural frequency of fractional order delay dynamic vibration absorber excitation frequency change. The study showed that the vibration amplitude of the main system can be reduced by increasing the amount of dynamic vibration absorber delay,in a certain range of time delay,under stable conditions of main system and the dynamic vibration absorber. The data simulation analysis proved that this new method is feasible. The vibration damping effect is obvious,vibration is reduced about 99% by the novel dynamic vibration absorber,it is almost completely absorption; Even though the passive vibration absorber is obviously reduced,the new type of dynamicvibration absorber is still maintained an 83% vibration absorption effect.

关 键 词：分数阶导数 时滞 反馈 动力吸振器 

分 类 号：O328[理学—一般力学与力学基础] TB123[理学—力学]