Research On Some Key Problems Of Nonlinear Energy Sink

Nonlinear Energy Sink（NES）has a simple structure,lightweight,and can achieve broadband vibration reduction,and has a wide range of application prospects.This article focuses on the three key problems in the application of nonlinear energy sink to carry out theoretical research,and strives to provide data support and theoretical reference for its application.First,in engineering research,in order to simplify the calculation,the vibration reduction system is usually linearized.Improper linearization will make a big difference between the calculated results and the actual response.Therefore,it is necessary to study the influence of the nonlinear factors of the damped system on the vibration reduction efficiency of the nonlinear energy sink.Second,the installation position of the NES in the damping system has a greater impact on its vibration reduction efficiency.It is worthy of research to determine the best position of the NES according to different situations to minimize the vibration of the primary structure.Third,the ungrounded series NES overcomes to a certain extent the problem that the vibration reduction efficiency of a single degree of freedom NES is severely reduced under large excitation,but whether the grounded series NES has higher vibration reduction efficiency still needs further research and analysis.The main contents are as follows:This paper firstly studies the difference and change law of NES’s vibration reduction effectiveness on nonlinear plates and linear plates under harmonic excitation and impact excitation.From the ordinary differential dynamic equation of the nonlinear plate connected to the NES,the slow-varying equation of the system is obtained by the complex variable averaging method,and then the nonlinear equation set describing the steady-state response is obtained,and then the Runge-Kutta method is used to verify the derived approximation system correctness.By comparing and analyzing the frequency response of the first two modes of the two plates,it is found that a larger amplitude of the harmonic excitation will cause the system to have a high branch response,which will then merge with the low branch response.With the increase of excitation amplitude,for different plate models,the vibration reduction effect of NES on the first-order mode will be several times different,and the difference in response to the second-order mode is mainly reflected in the difference in superharmonic resonance response.Under impact excitation,when the excitation amplitude is large,the NES has a difference in the vibration reduction efficiency of the two plates,and the difference between the vibration reduction efficiency will become larger as the excitation amplitude increases.For two different multi-degree-of-freedom primary structures,numerical methods are used to analyze the difference in vibration reduction efficiency caused by the position of NES,and to explore the best vibration reduction position of NES.When the NES is connected to the primary oscillators M₁,M₂,and M₃,the positions of the NES are marked as P₁,P₂,and P₃,respectively.The research results show that for the ungrounded three-degree-of-freedom primary structure,it is best to install the NES at the P₃position under impact excitation.For the vibration suppression of the grounded three-degree-of-freedom primary structure,the vibration suppression requirements for the primary structure under impact excitation are different,and the best placement position of the NES is different;while under the sweep frequency excitation,it is best to install the NES at the P₂position.For the damped grounded series NES and the ungrounded series NES with decreasing parameters,the difference in vibration reduction effectiveness of the two is analyzed by numerical methods.The research results show that,in a wider range of excitation amplitude,the damped grounded series NES has stronger vibration reduction efficiency.The difference in energy consumption of each NES in the series NES is analyzed,and it is found that the role of each NES in the series NES in the energy dissipation of the primary structure changes with the increase of the excitation amplitude.In addition,reasonably changing the parameters of NES can improve its vibration reduction efficiency.