赫兹链中孤波相互作用的实验证据
Experimental evidence of solitary wave interaction in Hertzian chains
摘要：
我们实验研究了两个孤立波之间的相互作用，接近一个到另一个在一个线性链的球体通过赫兹势相互作用。当这些反向传播的波碰撞时，它们彼此交叉，并且由于非线性相互作用势而引入相对于非相互作用波的相移。我们的数值模拟很好地再现了这一观察结果，它被证明是独立的粘弹性耗散珠接触。此外，当等振幅同步反向传播的波发生碰撞时，我们观察到两个次级孤立波从相互作用区域中产生。次级孤立波的振幅与入射波的振幅成正比。当碰撞发生在链的中间接触点时，偶数个珠子链的次级孤立波更强。虽然数值模拟正确地预测了这些波的存在，但实验表明它们各自的振幅明显大于预测。我们将这种差异归因于孤立波传播过程中珠接触处的滚动摩擦。
英文摘要：
We study experimentally the interaction between two solitary waves that approach one to another in a linear chain of spheres interacting via the Hertz potential. When these counter propagating waves collide, they cross each other and a phase shift respect to the noninteracting waves is introduced, as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and it is shown to be independent of viscoelastic dissipation at the beads contact. In addition, when the collision of equal amplitude and synchronized counter propagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitude are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the beads contacts during solitary wave propagation.
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