耦合组合刚度非线性能量阱的线性振子动力学分析

Dynamic analysis of linear oscillator with coupled combined stiffness NES

将非线性能量阱(NES)连接到线性或弱非线性结构能吸收振动能量以达到减少振动的目的,在被动减振中具有重要的意义。该研究对耦合组合刚度NES的线性振荡器进行了动力学建模和分析,并给出了NES系统参数对减振效果的影响。首先,利用复变量平均法对耦合组合刚度NES的系统进行建模,得到了系统的慢变方程。其次,分析了鞍结分岔和Hopf分岔平衡点个数、稳定性与组合刚度NES系统参数的关系,并给出了激励幅值、频率变化对线性振子幅值的影响,这为后面减振应用的优化提供合理的参数选值具有重要意义。再次,利用能量谱和Poincare映射分析了各部分质量比、激励幅值、NES刚度和阻尼对系统减振的影响,发现了各参数对振动抑制的影响规律。最后利用能量谱验证了组合刚度NES的减振的优越性。

Connecting nonlinear energy sink(NES)to linear or weakly nonlinear structures can absorb vibration energy to reduce vibration,which is of great significance in passive vibration reduction.Here,dynamic modeling and analysis were performed for a linear oscillator with coupled combined stiffness NES,and effects of NES system parameters on vibration reduction effect was studied.Firstly,the complex variable average method was used to establish the dynamic model of the system with coupled combined stiffness NES,and the slowly varying equations of the system were obtained.Secondly,relations among number of equilibrium points and stability of saddle node bifurcation and Hopf bifurcation,and parameters of combined stiffness NES system were analyzed,and effects of excitation's amplitude and frequency on amplitude of linear oscillator were studied,both of them were of great significance to provide reasonable parametric selection for optimization of later vibration reduction application.Thirdly,effects of each component mass ratio,excitation amplitude,NES stiffness and damping on system vibration reduction were analyzed by using the energy spectrum and Poincare mapping,and influence laws of various parameters on vibration suppression were found.Finally,the vibration reduction superiority of coupled combined stiffness NES was verified using the energy spectrum.