Dynamic Performance Analysis Of A System Coupled With Two-degree-of-freedom Nonlinear Energy Sink

Nonlinear energy sink(NES),as a passive vibration absorber,has the characteristics of targeted energy transition(TET),its additional mass is small and does not require additional energy,which has Wide application prospects in actual production.In this paper,a system with two-degree-of-freedom nonlinear energy sink is established to study the relationship between its structural parameters and its vibration damping performance and dynamic behavior.The specific work is as follows:A three-degree-of-freedom system coupled with two-degree-of-freedom nonlinear energy sink is established,and the motion differential equation of the nonlinear system is given,and the Taylor series expansion is used to approximate the nonlinear force experienced by the two oscillators.The numerical method is used to analyze the damping performance of the NES.From the perspective of its structural parameters and initial energy,the conditions for its targeted energy transfer are studied.It is found that the NES can effectively reduce the energy of the main structure,and its vibration suppression effect is significantly better than that of the single degree of freedom NES system.The differential equation of the system motion under simple harmonic excitation is transformed into an algebraic equation by the harmonic balance method,the steady-state amplitude-frequency response of the system is obtained,and the energy frequency diagram of the system when chaos occurs is obtained by numerical simulation,and the influence of vibration amplitude system parameter pair on vibration amplitude is analyzed.The Poincarémap is used to analyze the global bifurcation of the system with the spring stiffness as the bifurcation parameter,Combining the phase diagram and the Poincaré cross-section diagram to analyze the motion state of the system,it is found that the spring stiffness connecting the main structure and the primary vibrator has a greater impact on the vibration absorption performance and dynamic behavior.If the stiffness is too large or too small,it is not conducive to the damping performance NES system.When the system exhibits periodic motion and chaotic motion,its impact is different.With the change of the stiffness,the system exhibits complex dynamic behavior.Changing the original length of the spring connecting the primary and secondary vibrators in the two-degree-of-freedom non-linear energy sink makes the vibrator have two stable equilibrium points and one unstable equilibrium point,and the system shows the characteristics of negative stiffness(the force generated by the spring is the same as direction of motion),using numerical simulation methods to study the damping performance of the negative stiffness NES system,It is found that compared with the original two-degree-of-freedom NES,the negative stiffness NES shows a better targeted energy transfer effectThe gap between the first-order vibrator and the second-order vibrator in the two-degreeof-freedom nonlinear energy sink is limited,so that the two vibrators collide when vibrating.Combining the law of momentum conservation and the shock equation,the relationship between the speed changes of the two vibrators after collision is obtained.Using numerical simulation to analyze the damping performance of the collision NES,it is found that the collision NES has better vibration absorption effect than two-degree-of-freedom NES.As the gap between the two vibrators decreases and the number of collisions increases,the system’s damping performance improves.When the gap reaches a certain level,the gap continues to be reduced,and the damping performance remains unchanged.