#### Vol. 2, No. 8, 2007

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Elastic Wannier–Stark ladders in torsional waves

### Guillermo Monsivais, Rafael A. Méndez-Sánchez, Alfredo Díaz de Anda, Jorge Flores, Luis Gutiérrez and Alejandro Morales

Vol. 2 (2007), No. 8, 1629–1638
##### Abstract

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 nearest-neighbor 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 $\gamma$ 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.