We report on the observation of Wannier-Stark ladders in the bending vibrations of elastic beams. By introducing a gradient in the length distribution of N weakly coupled beams, the elastic equivalent of the Wannier-Stark ladder is obtained in a system governed by two coupled second-degree differential equations, instead of the common wave equation, and whose oscillations are also dispersive and, above a certain critical frequency, occur with two wavelengths. We have measured for the first time, not only the spectrum of the ladders, but the wave amplitudes in this type of system, which are not directly accessible in quantum-mechanical systems, and we have found that the wavelengths are spatially localized and in good agreement with the theoretically predicted amplitudes. Due to the combination of differential equations and the boundary conditions imposed on the system, the Wannier-Stark ladder phenomenon occurs from the third band of states onwards, unlike other classical systems.

我们报告了对弹性梁弯曲振动中 Wannier-Stark 梯子的观察。通过在N的长度分布中引入梯度在弱耦合梁中，Wannier-Stark 阶梯的弹性等效是在由两个耦合的二阶微分方程而不是普通波动方程控制的系统中获得的，并且其振荡也是色散的，并且在某个临界频率以上时会发生有两个波长。我们第一次不仅测量了梯子的光谱，而且测量了这种类型系统中的波幅，这在量子力学系统中是无法直接获得的，我们发现波长在空间上是局部化的，并且很好与理论预测的幅度一致。由于微分方程和施加在系统上的边界条件的组合，与其他经典系统不同，Wannier-Stark 阶梯现象从第三态带开始出现。