Parameter Design And Dynamic Analysis Of Impacting Dynamic Vibration Absorber

As a common way to reduce vibration in the field of vibration control,dynamic vibration absorber has achieved a lot of theoretical research results.In recent years,the development of dynamic vibration absorber has been enriched by the application of new technologies and materials such as grounded stiffness,inerter and lever.In engineering practice,the limitation of installation space may lead to new issues such as impacting.The vibro-impact systems have been widely studied by many scholars due to their complex dynamic behavior.Impacting dynamic vibration absorber is a passive damping device considering impact energy consumption,which is often used to suppress the vibration of bridges and submarine pipelines.The main content of this thesis consists of the following parts:(1)A new type of grounded dynamic vibration absorber model is established,which simultaneously contains grounded stiffness,inerter and lever.Based on the fixed point theory,the optimal analytical solution and control performance have been studied.The proper grounded stiffness,inerter and lever were introduced into the traditional grounded damping dynamic vibration absorber,and its parameters were optimized based on the H∞ optimization criterion.This method requires minimizing the peak value of the amplitude-frequency response curve of the main system to calculate the corresponding frequency ratio,damping ratio,grounded stiffness ratio and the working range of the inerter,so as to achieve the optimal control effect.(2)A vibro-impact model under harmonic external excitation was established to study the bifurcation behavior of Duffing oscillator with fractional derivative under unilateral and bilateral constrains.Based on the Melnikov method for vibro-impact systems,the homoclinic orbit bifurcation of the system was discussed,and the necessary conditions for the chaos to occur in the sense of Smale horseshoe was calculated.The dynamic behavior of the system with changes in parameters such as fractional order,collision gap,amplitude and the frequency of external excitation were analyzed in detail.(3)A model of impacting fractional order dynamic vibration absorber was established to study the vibration reduction performance under harmonic external excitation.Based on the fixed point theory,the parameter optimization of the fractional-order dynamic vibration absorber without impacting was performed.The design formulas for the optimal frequency ratio and damping ratio were derived,and the optimal fractional order and coefficient formulas were obtained.The frequency ratio and damping ratio were not the sensitive parameters which could affect the vibration reduction effect,while the gap ratio and recovery coefficient were two sensitive parameters.Under the optimal parameters,the impacting fractional order dynamic vibration absorber can not only save space,but also has better damping performance under most external excitation frequencies.The main research content was summarized in the end,and the urgent problems that need to be solved in future research were prospected,which provides ideas and suggestions for future research.