In this paper, the low-frequency flexural wave band gap and broadband vibration reduction characteristics of multi-scale elastic metabeams with particle damping are theoretically and numerically studied. A band gap theoretical prediction model of multi-scale elastic metabeams with particle damping is established by using the plane wave expansion method combination with the gas-particle two-phase flow theory. Besides, a fully time-domain bidirectional coupling method of the discrete element method (DEM) combination with multi-flexible body dynamics (MFBD) is proposed to investigate the vibration transmission and particle motion as well as energy dissipation characteristics. In addition, the vibration transmission tests of multi-scale elastic metabeams with particle damping were conducted to validate the theoretical prediction model and simulation model. Furthermore, the influence of particle diameter and excitation intensity are investigated. Results show that the band gap theoretical model of multi-scale elastic metabeams with particle damping can accurately and effectively predict the band structure and elastic wave attenuation characteristics. The low frequency broadband vibration suppression can be achieved by coupling the broadband vibration reduction mechanism of particle damping and the low frequency band gap mechanism of the elastic metabeams. The coupling of particle damping and elastic metabeams exhibits three typical stages in vibration suppression: strong positive coupling, negative coupling and weakened positive coupling.

中文翻译：

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具有粒子阻尼的多尺度弹性超光束的低频带隙预测和宽带减振

本文对具有粒子阻尼的多尺度弹性超光束的低频弯曲波带隙和宽带减振特性进行了理论和数值研究。采用平面波展开法与气粒两相流理论相结合，建立了具有粒子阻尼作用的多尺度弹性超光束带隙理论预测模型。此外，提出了一种离散元法 （DEM） 与多柔性体动力学 （MFBD） 相结合的全时域双向耦合方法，以研究振动传递和粒子运动以及能量耗散特性。此外，还进行了具有粒子阻尼的多尺度弹性超光束的振动传递测试，以验证理论预测模型和仿真模型。此外，还研究了颗粒直径和激发强度的影响。结果表明，具有粒子阻尼的多尺度弹性超光束带隙理论模型能够准确有效地预测能带结构和弹性波衰减特性。通过将粒子阻尼的宽带减振机构与弹性超光束的低频带隙机构耦合，可以实现低频宽带减振。粒子阻尼与弹性超光束的耦合在振动抑制中表现出三个典型的阶段：强正耦合、负耦合和弱正耦合。