论文标题
在有限长度的颗粒链中发生逐渐共振的发生
Occurrence of gradual resonance in a finite-length granular chain driven by harmonic vibration
论文作者
论文摘要
这项研究介绍了由和谐振动管驱动的有限长度颗粒链的共振的数值模拟。确定了多种逐渐谐振模式，即非共振模式，部分共振模式和完整共振模式。随着固定的振动频率，增加的振动加速会导致参与共振的晶粒数量增加，这等于振动期间的晶粒碰撞数量。与晶粒谷物和谷物壁碰撞的特征时间相比，自由飞行时间在谷物运动中起主要作用。这种情况导致晶粒与独立的晶粒谷物和增益壁碰撞之间发生较大的开放缝隙。描述系统能量对颗粒链长度的依赖性和晶粒碰撞数量的一般主方程，并且与模拟结果非常吻合。当振动加速度不断增加时，我们观察到系统能量的逐步增加，这是针对单个能量注入的。此外，在$ ϕ- \itγ$和$ n- \itγ$的空间中讨论了两个典型的相图。
This study presents numerical simulations of the resonance of a finite-length granular chain of dissipative grains driven by a harmonically vibrated tube. Multiple gradual resonant modes, namely, non-resonance mode, partial-resonance mode, and complete-resonance mode, are identified. With a fixed vibration frequency, increased vibration acceleration leads to a one-by-one increase in the number of grains participating in resonance, which is equal to the number of grain-wall collisions in a vibration period. Compared with the characteristic time of the grain-grain and the grain-wall collisions, the time of free flight plays a dominant role in grain motion. This condition results in the occurrence of large opening gaps between the grains and independent grain-grain and gain-wall collisions. A general master equation that describes the dependence of the system energy on the length of the granular chain and the number of grain-wall collisions is established, and it is in good agreement with the simulation results. We observe a gradual step-jump increase in system energy when the vibration acceleration is continuously increased, which is dedicated to an individual energy injection. Moreover, two typical phase diagrams are discussed in the spaces of $ϕ-\itΓ$ and $N-\itΓ$.
