Design,Modeling,Analysis And Experimental Research Of Limited Nonlinear Absorber

Nonlinear energy sink(Nonlinear energy sink,NES)has excellent performance in vibration control due to its energy directional transfer mechanism and resonance capture characteristics.However,since the NES does not contain linear stiffness,the amplitude of the NES may be larger,which may cause structural instability and hinder the engineering application of the NES.Therefore,the vibration of NES needs to be controlled.In this paper,several kinds of limiting strategies are designed to control the vibration amplitude of NES.Moreover,with the help of intelligent optimization algorithm,the parameters of limited nonlinear shock absorber are designed to enhance the structural reliability and improve the vibration damping performance of the nonlinear shock absorber.This work can provide a useful guidance for the design of the NES.Meanwhile,it is of great significance to broaden the application of the NER in the engineering field.The concrete contents are as follows:(1)A grounded piecewise nonlinearity is introduced into the traditional NES,the limited NES is designed to limit the amplified NES.Based on Newton’s second law,a theoretical model is established.The effect of piecewise stiffness and clearance on the vibration response of the NES and the linear oscillators under transient respionse is significantly disscussed.The particle swarm optimization algorithm is used to optimize parameters of the limited NES.Furthermore,the particle swarm optimization results are compared with the differential evolution algorithm results,which verifies the correctness of the optimization results.The experimental platform of amplitude limited NES is constructed and the system parameters are identified.The comparison between experimental results and theoretical results shows that it can effectively suppress the vibration amplitude of NES and enhance the vibration damping performance of the NES.(2)Based on design of the limited NES,the steady-state response dynamic characteristics are investigated.The piecewise nonlinearity is introduced into the limited NES,which makes it difficult to obtain the approximate analytical solution of the steady-state response of the system.The method of fitting piecewise stiffness by continuous hyperbolic tangent function is proposed,and the approximate analytical analysis method of steady-state response of piecewise system is developed.The approximate analytical results are verified by numerical simulation and experimental research.The results show that the appropriate limit stiffness can effectively suppress the vibration of the NES,while maintaining a good vibration reduction effect,and reduce the cost of vibration reduction by reducing the weight of the NES.(3)Magnetic force is introduced to limit the vibration of the NES,and the magnetically enhanced NES is designed.According to the repulsive force of the permanent magnet,the expression of the nonlinear magnetic force is derived.Based on the dynamic equations of the coupled system,the harmonic balance method and numerical simulation method are used to obtain the coupled vibration response of the linear oscillator and the NES.The effects of magnetic gap,magnetic intensity and external excitation intensity on the coupled vibration of linear oscillator and NES are revealed.The corresponding experiments are carried out to confirm that the proposed structure can limit the NES in a certain range and improve the vibration damping performance of the NES.(4)A piecewise stiffness is introduced between the NES and the primary system.Based on the coupled dynamic equations,the effects of piecewise stiffness and clearance on the vibration suppression effect of the NES under the transient response and the steady-state response are discussed.The differential evolution algorithm is used to optimize the parameters of the piecewise nonlinearity and the optimal parameters are obtianed.Theoretical and experimental results show that the vibration suppression effect of the encapsulated NES is better than that of the traditional NES in most parameters.The vibration of the NES can limited by the encapsulated NES in a certain range,while the damping efficiency of the encapsulated NES can reach more than 90%.(5)The piecewise damping is introduced into the design of the encapsulated NES,and an encapsulated NES with limited damping is constructed.A two-degree-of-freedom non-smooth nonlinear dynamic model of the encapsulated NES with limitrd damping and stiffness is established.A nonsmooth function describing piecewise damping and stiffness is fitted by hyperbolic tangent function.The effect of the piecewise stiffness,the piecewise damping and clearance on the vibration reduction effect of the NES is discussed by approximately analytically.The experiment verifies the effectiveness and correctness of the theoretical analysis,and proves that the introduced damping is helpful to the dissipation of vibration energy.Moreover,a multi-objective optimization strategy for two-modal vibration control is proposed to achieve efficient passive control of the two resonance peaks.Overall,the limited nonlinear absorber device proposed in this paper has the characteristics simple structure,small added mass and high damping efficiency,which has a very high application prospect.