Investigation Of Vibration Control And Propagation Based On Nonlinear Coupled System

It is an important research direction in vibration reduction field to improve the passive control performance of vibration system by employment of nonlinear characteristics.The vibration suppression system with different geometric configurations should be designed for different working conditions.In this paper,we study the influence of nonlinear features on the vibration control and the propagation of elastic waves for two coupled systems with nonlinear structures.For the systems with nonlinear absorbers,the complex nonlinear dynamics and vibration reduction performance of the structure have been studied under different internal resonances states.For nonlinear metamaterial beam structures,the effect of internal resonances on the nonlinear vibration transmissibility has been investigated.And the dispersion properties have been analyzed under different coupling conditions of high order harmonics.The specific research contents are as follows:(1)A vibration suppression system with X-shaped internal resonance absorber is designed.Nonlinear coupled systems have been modeled by energy methods,and the dynamical and vibration properties of nonlinear vibration absorbers have been studied numerically,analytically and experimentally.The system will exhibit various internal resonances by adjusting the structural parameters.Under the condition of 3:1 internal resonance,the global bifurcation diagram of the vibration system was obtained.And the periodic,periodic doubling,and chaotic motions were analyzed.The influences of the rod length and initial angle of the nonlinear oscillator on the vibration response were revealed.The amplitude-frequency response curve obtained by the theoretical formulation,as well as the periodic and periodic doubling motion states,were experimentally verified.(2)By comparing the vibration amplitude of the main system in the resonance region with or without the absorber,it was found that the designed absorber could exert the nonlinear characteristics of internal resonance and achieve efficient vibration control.The amplitude-frequency response of the main system is studied under 1:2 and 1:3 internal resonances.It is shown that the amplitude of the oscillations of the primary system can be greatly reduced in the vicinity of the primary resonance region.It has also been found that vibration suppression systems with absorbers will exhibit saturation features,which could improve the vibration suppression effect of the main structure.In addition,The dynamic responses under two internal resonance states were obtained through vibration experiments,and the experimental results were in good agreement with the numerical results,verifying the accuracy of the theoretical results and the effectiveness of enhancing the vibration reduction effect by internal resonance.(3)The band structure of the finite size metamaterial beam structure with X-shaped nonlinear oscillators was calculated by the equivalent medium method,modal superposition method,and finite element simulation.And the vibration propagation characteristics were discussed.In addition to the verification of the band structure,the influence of internal resonance on the vibration transmissibility of the structure was studied.It was found that the vibration reduction effect would decrease when the ratio between the linearized natural frequency of the resonator and the natural frequency of the basic beam increased.The influence of the mass of the additional oscillators and excitation amplitude on the mean transmissibility of nonlinear vibration are discussed.(4)The elastic wave propagation properties of a semi-infinite metamaterial beam with X-shaped nonlinear resonator were studied by the equivalent medium theory.The nonlinear dispersion characteristics under the force and displacement regulations are discussed respectively.The effect of the rod initial angle of nonlinear oscillator on the equivalent dynamic mass density was discussed.It was found that there is a transition from soft to hard nonlinear feature as the initial angle changed.In addition,the influence of the coupling of fundamental wave and higher order harmonics on elastic wave propagation were discussed under displacement regulation.The results show that the coupling of the higher order harmonics will reduce the attenuation rate of the fundamental wave.The physical variables which partly depends on the equivalent dynamic mass density,such as wave velocity,wave vector,band gap,etc.are closely related to the amplitude.Therefore,the objective of widening the band gap interval can be achieved by tuning the amplitude.