Complex Variable Perturbation Method For NES With Negative Stiffness

Nonlinear energy sink(NES)technology aims to absorb and dissipate the response energy of the main structure by using the oscillator with strong non-linear stiffness as an additional substructure through the internal resonance behavior generated by the additional substructure and the main structure.Because the internal resonance can be generated in a wider frequency domain,NES has better absorption band and performance robustness.In this paper,the mechanism and internal resonance form of NES with negative stiffness are studied.The perturbation solution of NES with negative stiffness is analyzed by using complex variable perturbation method.The internal resonance capture behavior of NES system is theoretically studied and demonstrated.The specific innovations and work contents include:(1)The internal resonance behavior of NES undamped free vibration with negative stiffness is studied.The perturbation solution of internal resonance is analyzed.The influence of system energy,negative stiffness term and positive stiffness on the internal resonance law is analyzed by using the perturbation solution.The results show that the increase of system energy will lead to the transition of internal resonance form to higher order,and the increase of negative stiffness will lead to the transition of internal resonance form to lower order.The1:3 harmonic internal resonance of NES and main structure is the more active form of internal resonance of the system.(2)Based on the perturbation solution of 1:3 internal resonance,the optimization parameters of NES with negative stiffness are analyzed.Several types of NES with negative stiffness are proposed by using the combination of spring and space magnetic force to simulate the vibration control performance.The results show that the control performance of NES with negative stiffness is better than that of NES with cubic nonlinearity,and therobustness of NES with negative stiffness to the dynamic characteristics and seismic peak changes of the main structure is better than that of TMD and NES with cubic nonlinearity.It is shown that NES with negative stiffness designed by 1:3 internal resonance excellent parameters has better seismic control performance.(3)In order to further study the working mechanism of negative stiffness NES,the seismic response time history of the structure system is analyzed by numerical wavelet transform.The results show that the internal resonance capture behavior of negative stiffness NES mainly depends on the transient sub-harmonic internal resonance capture behavior.Compared with TMD and cubic non-linear NES,this behavior can be generated in a wider frequency domain and lasts longer.Because this resonance capture behavior is insensitive to the fundamental frequency change of the main structure,it has better robustness.