杠杆型非线性耗散弹性超材料的宽频振动抑制方法研究

Broadband vibration suppression method of lever-type nonlinear dissipative elastic metamaterials

  • 摘要: 杠杆型弹性超材料相对于传统的纯质量弹簧系统具有良好的可调谐性,通过调整杠杆比可以有效地调整带隙的宽度和位置。为了拓宽被动隔振系统的减振带宽,通过在杠杆型弹性超材料中引入非线性和耗散阻尼,提出了一种杠杆型非线性耗散弹性超材料。本文通过摄动法推导了非线性频散关系的显式表达式,并研究了不同非线性组合对非线性非耗散超材料能带结构的影响;探讨了结构参数对非线性频散曲线和带隙宽度、位置的影响;构建了杠杆型非线性耗散弹性超材料有限结构,并采用数值方法对其瞬态波传播进行了仿真实验,探讨可产生更宽弹性波衰减区域的非线性和阻尼参数。数值结果表明,该杠杆型非线性耗散弹性超材料的弹性波衰减区域相对于线性非耗散弹性超材料增大了81.3%。

     

    Abstract: Lever-type elastic metamaterials have good tunability relative to conventional pure mass-spring systems, and the width and position of the bandgap can be effectively adjusted by adjusting the lever ratio. In order to broaden the vibration reduction bandwidth of the passive vibration isolation system, a lever-type nonlinear dissipative elastic metamaterial is proposed by introducing nonlinear and dissipative damping into the lever-type elastic metamaterial. This paper derives an explicit expression of the nonlinear dispersion relation using the perturbation method and investigates the band structure of nonlinear non-dissipative metamaterials with different nonlinear combinations. The effects of structural parameters on the nonlinear dispersion curves and the width and position of the band gaps are explored. A finite structure of lever-type nonlinear dissipative elastic metamaterials is constructed and various tests of its transient wave propagation are performed by numerical integration method to explore the nonlinear and damping parameters that can produce a wider elastic wave attenuation region. Numerical results show that the elastic wave attenuation region of this lever-type nonlinear dissipative elastic metamaterial increases by 81.3% with respect to the linear nondissipative metamaterials.

     

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