Research On Dynamic Characteristics Of Vibration Reduction System Based On Nonlinear Energy Sink

Spacecraft encounter complex dynamic environments during service,which can lead to harmful vibrations that affect their normal work and operation.Effective vibration suppression for spacecraft is of great significance to ensure their normal work and operation.Passive vibration suppression methods have received widespread research and application due to their advantages such as simple structure,low cost,and easy maintenance.This paper conducts relevant research on the vibration suppression performance of a typical passive vibration control device,which is a nonlinear energy sink(NES).The specific research content is as follows:The vibration reduction performance of the cubic damping NES system considering the effect of frequency detuning is studied.Firstly,the bifurcation response of the system is analyzed using the complex variable averaging method,obtaining the characteristics of saddle node bifurcation and Hopf bifurcation,indicating the influence of different frequency detuning coefficients and NES parameters on the bifurcation response of the system,and revealing that cubic damping NES can eliminate the high amplitude response branches under linear damping NES.Secondly,the multi-scale method is applied to study the strongly modulated response(SMR)of the system,and the influence law of the external excitation amplitude on the frequency detuning coefficient interval where the SMR exist is further illustrated through one-dimensional mapping.Finally,the energy spectrum,Poincare mapping and time response are applied to analyze the vibration suppression of the cubic damping NES,obtaining the influence of NES parameter changes on the vibration reduction,and revealing the advantages of the NE S with cubic nonlinear damping in vibration suppression.In order to further improve the vibration reduction effect of NES,a combined stiffness NES model is proposed and the dynamics of the combined stiffness NES system is analyzed.Firstly,by studying the bifurcation response of the motion equation of the combined stiffness NES system,the influence of the combined stiffness ratio on the saddle-node bifurcation,Hopf bifurcation and amplitude response of the system is revealed.Secondly,through the study of the SMR of the combined stiffness NES system,the influence law of different combined stiffness ratios on the invariant manifold and the frequency detuning interval with SMR is shown.Finally,the vibration suppression effect of combined stiffness NES is studied through energy spectrum,revealing the influence rule of stiffness ratio change on the energy of the main structure,indicating that combined stiffness NES has better vibration suppression effect than cubic stiffness NES.To improve the vibration suppression effect of NES under complex external excitation,a combined damping and combined stiffness NES model is proposed,and its vibration suppression performance under harmonic excitation or impulsive load is studied.On the one hand,the dynamic response of the combined damping NES system under simple harmonic excitation are studied,revealing the influence law of the damping ratio of the combined damping NES on the bifurcation response,amplitude response,SMR of the system.Meanwhile,the energy spectrum is used to analyze the vibration suppression effect of the combined damping NES,obtaining the influence of different damping ratios of the combined damping NES on the vibration suppression effect,and revealing that the combined damping NES has better vibration reduction effect than the cubic damping NES.On the other hand,On the other hand,the vibration reduction effects of different damping NES under different impulsive load amplitudes are analyzed,discovering the differences in vibration suppression effects between linear damping NES and cubic damping NES under different shock excitation amplitudes,indicating that the combined damping NES has better vibration reduction effects under different impulsive load amplitude.To extend the degrees of freedom of NES,a 2-dof NES model with combined damping and stiffness is proposed and the dynamics of the 2-dof NES system is studied.Firstly,the analysis of a 2-dof NES system without considering the effect of frequency detuning is analyzed,indicating the influence of external excitation amplitude and 2-dof NES parameters on the bifurcation response of the system.Meanwhile,the incremental harmonic balance method and Floquet theory are applied to study the response amplitude and stability of a 2-dof NES system considering frequency detuning effects,revealing that 2-dof NES can reduce the response amplitude of the main structure.Then,the SMR analysis is conducted on the 2-dof NES system,obtaining that the 2-dof NES system can generate additional SMR than the 1-of NES system,revealing that the response of each component of the 2-dof NES system is no longer consistent.Finally,the vibration suppression effect of 2-dof NES is studied,indicating the changes brought by 2-dof NES to the system vibration suppression effect,and revealing that 2-dof NES has better vibration suppression effect than 1-of NES.The finite element method is introduced to conduct relevant application research on the NES cantilever beam.Firstly,the response of the NES cantilever beam system is analyzed,indicating the influence law of the external excitation position and the NES position on the system response,revealing the response of NES and cantilever beam is consistent.Secondly,the vibration suppression of NES under different excitation frequencies is studied,indicating the vibration suppression effect of NES on the cantilever beam system,revealing that reasonable design of NES parameters is beneficial for improving the vibration reduction effect of NES on the cantilever beam.Finally,the vibration suppression effects of different 1-dof NES in this paper are compared and analyzed,indicating that the combined stiffness and combined damping NES has good vibration reduction effects under different NES parameters.