Study On Energy Transfer And Vibration Suppression Of Coupled Non-smooth Stiffness NES System

Nonlinear Energy Sinks(NES)developed in recent years have good engineering application prospects due to their high vibration suppression efficiency and strong robustness under specific conditions,and are gradually attracting the attention of scholars.This thesis mainly studies a class of NES with piecewise linear stiffness or a combination of piecewise linear stiffness and cubic stiffness,that is,non-smooth stiffness NES.The energy transfer efficiency and energy dissipation of the system are studied by the parameter analysis of coupled piecewise linear stiffness NES and coupled combined stiffness NES,and the vibration suppression of system parameters and noise intensity on coupled piecewise linear stiffness NES system under Gaussian white noise excitation is discussed.The specific content is summarized in the following aspects:Firstly,the energy transfer efficiency and energy dissipation of coupled piecewise linear stiffness NES system are studied,the slow-varying equation of coupled piecewise linear stiffness NES system is solved by the complex variable-average method,and the approximate function of the unstable point in the slow invariant manifold graph of the system is solved by polynomial approximation,so as to establish the energy transfer efficiency equation of coupled piecewise linear stiffness NES and analyze the influence of gap and piecewise stiffness on energy transfer efficiency.Based on the system slow change equation,the energy dissipation equation of the coupled piecewise linear stiffness NES system is derived,and then the relationship between the damping coefficient of the main structure and the dissipation time is analyzed,and the numerical simulation shows that the larger the gap of the piecewise linear stiffness NES,the lower the energy transfer efficiency of the system,the greater the piecewise linear stiffness,the higher the energy transfer efficiency of the system,and it is derived from the dissipation equation that the dissipation time of the coupled piecewise linear stiffness NES system to the main structure energy is much smaller than the energy dissipation time of the original system when the damping ratio is the same.And with the increase of the damping coefficient of the segmented linear stiffness NES,the system dissipation time gradually decreases.Secondly,the piecewise linear stiffness is added to the traditional coupled cubic stiffness NES system,the slow-varying equation of the coupled combined stiffness NES system is solved by the complex variable-average method,and the approximate function of the unstable point in the slow invariant manifold graph of the system is solved by the polynomial approximation method,so as to establish the energy transfer efficiency equation of the coupled combined stiffness NES system,and the effects of gap and piecewise stiffness and cubic stiffness terms on the energy transfer efficiency of the system are analyzed.The energy dissipation equation of the coupled combined stiffness NES system is derived,the relationship between system damping and structural parameters when energy transfer occurs in the system is discussed,and the relationship between the damping coefficient of the main structure and the dissipation time is analyzed.The numerical simulation shows that the energy transfer efficiency of the system gradually decreases with the increase of the gap of the combined stiffness NES,and the energy transfer efficiency of the system gradually increases with the increase of the segmented stiffness of the combined stiffness NES,and it is found that the change of cubic stiffness has little effect on the energy transfer efficiency of the system.When the damping ratio is the same,the energy dissipation time of the coupled combined stiffness NES system is much smaller than that of the original system,and the energy dissipation time is smaller than that of the coupled segmented linear stiffness NES system,which indicates that adding segmented linear stiffness to the coupled combined stiffness NES system can improve the vibration suppression ability of the system,and the system dissipation time decreases with the increase of the combined stiffness NES damping coefficient.Finally,the Legendre polynomial approximation method is used to approximate and fit the piecewise linear stiffness function,and a polynomial function is obtained,and a model of coupled piecewise linear stiffness NES system excited by Gaussian white noise is established.The generalized harmonic function method is used to solve the equation,the finite difference method is used to solve the steady-state FPK equation of the system,and the results of the finite difference method are compared with the numerical solution by numerical simulation,and the two fit is very good,which proves the effectiveness of the finite difference method for solving the steady-state FPK equation of the system,and then analyzes the influence of system parameters and Gaussian white noise intensity on the probability density curve of system displacement and velocity shift,and the results show that The segmented linear stiffness NES excited by Gaussian white noise has a good damping effect on the main structure,but there will be random bifurcation phenomenon,which affects the stability of the system,by changing the parameters of the system structure,the transfer probability density curve may show unimodal or bimodal peaks,and the distance between the two peaks will affect the possibility of random jumps in the structure,and the occurrence of bimodal will also affect the random stability of the system.