结构弹性梁中的机械彩虹捕获和Bloch振荡
Mechanical Rainbow Trapping and Bloch Oscillations in Structured Elastic Beams
摘要：
我们从实验和数值两方面证明了在啁啾机械光束中传播的扭转波的机械彩虹捕获效应和机械布洛赫振荡。经过大量的模拟，三个准一维啁啾结构的设计，构造和实验特性的多普勒光谱。当啁啾强度为零时，得到一个具有带隙的理想周期系统。机械彩虹捕获效应发生的啁啾强度的小值。沿波束传播的波包逐渐变慢，并在一定深度处被反射回来，这取决于其中心频率。在这种情况下，出现了一种新的振荡，这里称为“{ \em整流彩虹-布洛赫振荡}"，因为波包在一侧被结构和均匀杆之间的界面反射，而在相对侧被小间隙反射。对于较大的啁啾参数值的彩虹捕获产生的机械布洛赫振荡出现的穿透长度。基于传递矩阵法的数值模拟结果与实验数据吻合较好。
英文摘要：
We demonstrate, both experimentally and numerically, the mechanical rainbow trapping effect and the mechanical Bloch oscillations for torsional waves propagating in chirped mechanical beams. After extensive simulations, three quasi-one-dimensional chirped structures were designed, constructed and experimentally characterized by Doppler spectroscopy. When the chirp intensity vanishes a perfect periodic system, with bands and gaps, is obtained. The mechanical rainbow trapping effect occurs for small values of the chirp intensity. The wave packet traveling along the beam is progressively slowing down and is reflected back at a certain depth, which depends on its central frequency. In this case a new kind of oscillation, here named "{\em rectified rainbow-Bloch oscillation}", appears since the wave packet is reflected at one side by the interface between the structure and the uniform rod and by the minigap at the opposite side. For larger values of the chirp parameter the rainbow trapping yields the penetration length where the mechanical Bloch oscillations emerge. Numerical simulations based on the transfer matrix method are in agreement with experimental data.
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