Mechanical Rainbow Trapping and Bloch Oscillations in Chirped Metallic Beams

The mechanical rainbow trapping effect and the mechanical Bloch oscillations for torsional waves propagating in chirped mechanical structures are here experimentally demonstrated. 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 is experimentally characterized for small values of the chirp intensity. The wave packet traveling along the structure is progressively slowing down and is reflected back at a certain depth, which depends on its central frequency. For larger values of the chirping parameter the rainbow trapping yields the penetration length where the mechanical Bloch oscillations emerge. Numerical simulations based on the transfer matrix method show an excellent agreement with experimental data.