Elastic Wannier–Stark ladders in torsional waves

We study the normal modes of torsional waves in an elastic beam consisting of a set of N cuboids of varying heights.We present experimental, theoretical, and numerical results.We show that some analogies to the Wannier-Stark ladders resonances, originally introduced by Wannier in 1962, are exhibited by this classical system.The original ladders studied by Wannier consist of a series of equidistant energy levels for the electrons in a crystal in the presence of a static external electric field with the nearestneighbor level spacing proportional to the intensity of the external field.For the case of torsional waves in the beam we have observed a similar behavior, namely, the vibrations of the beam show resonances of equidistant frequencies with the nearest-neighbor spacing proportional to parameter γ associated with the geometry of the beam analogously to the electric field.However, this analogy is not perfect; we address the origin of the differences.