具有几何非线性刚度的非线性能量阱振动抑制与动态特性研究

RESEARCH ON VIBRATION SUPPRESSION AND DYNAMIC CHARACTERISTICS OF NONLINEAR ENERGY SINK WITH GEOMETRIC NONLINEAR STIFFNESS

  • 摘要: 非线性能量阱(nonlinear energy sink, NES)作为一种被动控制策略,展现出强大的宽频减振性能,然而如何将其有效地应用于工程实际依然有待研究。为实现其潜在工程应用,提出了基于弹簧几何非线性的非线性能量阱,具备可控的线性与非线性刚度。阐述了非线性能量阱的实施方案,建立了具有非线性能量阱系统的非线性控制方程,在求解过程中,采用复变量平均法和数值方法求解系统的动态特性,基于主系统的振幅以及能量耗散率评估非线性能量阱在谐波激励下的减振性能,利用时程图、相位图探究主系统在不同参数以及初始条件下的动态特性。结果表明:通过合理控制NES质量比、弹簧刚度、阻尼等系统参数,非线性能量阱能够有效抑制主系统共振幅值。改变非线性能量阱的附加质量,主系统共振区状态呈现出周期响应、强调制响应以及混沌响应;在不同初始条件下,主系统具有多种稳态响应。

     

    Abstract: As a passive control strategy, nonlinear energy sink (NES) shows a strong broadband vibration reduction performance. However, how to effectively apply it to engineering practice remains to be studied. In order to realize its potential engineering application, a nonlinear energy sink based on spring geometric nonlinearity is proposed, which has controllable linear and nonlinear stiffness. The implementation scheme of the nonlinear energy sink is described, and the nonlinear control equation of the system with nonlinear energy sink is established. In the solution process, the complex variable averaging method and numerical method are used to solve the dynamic characteristics of the system. The vibration reduction performance of the nonlinear energy sink under harmonic excitations is evaluated by the basis of the amplitude and energy dissipation rate of the main system. The dynamic characteristics of the main system under different parameters and initial conditions are explored using time history diagrams and phase diagrams. The results show that by reasonably controlling the system parameters such as NES mass ratio, spring stiffness, damping, and the nonlinear energy sink can effectively suppress the resonance amplitude of the main system. By changing the additional mass of the nonlinear energy sink, the state of the main system in the resonance zone presents periodic response, strong modulation response, and chaotic response. Under different initial conditions, the main system has a variety of steady-state responses.

     

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