| Vibration control is an important problem in engineering.If the vibration is not controlled in most scenes,great losses will be caused to personnel safety,production activities and economy,etc.The traditional vibration control theory has limited effect in solving more complex problems.Therefore,the nonlinear vibration control theory has become a hot topic studied by scholars at home and abroad.As an efficient vibration control technology proved by many scholars at home and abroad,quasi-zero stiffness has good research value.The research content of this thesis includes:Firstly,an X-shape quasi-zero stiffness mechanism is constructed,its static characteristics are analyzed,and applied to the vibration isolation system with single degree of freedom.The dynamics model of the system under single frequency excitation is established.The approximate solution of the system’s period 1 motion is calculated based on the incremental harmonic balance method,and the jumping and cycle doubling bifurcations of the system are analyzed by using Floquet theory to calculate the stability.The approximate solution and stability of the periodic motion of the system are calculated,and the relationship between the bifurcation of the displacement response and the excitation amplitude is calculated.In addition,the effects of the parameters of the X-shape quasi-zero stiffness mechanism on the vibration isolation performance of the system under single frequency excitation are calculated.Secondly,based on the incremental harmonic balance method,the approximate solution and stability of the X-shape quasi-zero stiffness vibration isolation system with single degree of freedom are calculated when the frequency ratio is 1:2 and 1:3,respectively.The jumping and period-doubling bifurcation are analyzed,and the approximate solution and stability of the period 3 motion of the system are calculated,and the relationship between the period 3 motion and the excitation amplitude is analyzed.In addition,the influence of the parameters of the X-shape quasi-zero stiffness isolator on the vibration isolation performance of the system under dualfrequency excitation is calculated.Furthermore,a two-degree-of-freedom dynamic model with X-shape quasi-zero stiffness absorbing vibration is established.Based on the incremental harmonic balance method,the approximate solution and stability of the motion of period 1under single frequency excitation are calculated.The jumping and period-doubling bifurcations in the system are analyzed,and the approximate solution and stability of the motion of period 2 are calculated.The relationship between the displacement response bifurcation at the peak frequency of resonance and the excitation amplitude is analyzed.In addition,the influence of X-shape quasi-zero stiffness vibration absorber parameters on the vibration absorption effect under single frequency excitation is calculated.Finally,based on the incremental harmonic balance method,the approximate solution and stability of the two-degree-of-freedom dynamic model with X-shape quasi-zero stiffness vibration absorption under the double frequency excitation of 1:2and 1:3,respectively,were calculated.The jumping and period-doubling bifurcation were analyzed,and the approximate analytical solution of the period-doubling motion of the system was calculated.The relationship between the system displacement response bifurcation and excitation amplitude is calculated.In addition,the influence of X-shape quasi-zero stiffness vibration absorber parameters on the vibration absorption effect of the system under dual-frequency excitation is calculated. |
