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We demonstrate, both experimentally and numerically, the mechanical rainbowtrapping effect and the mechanical Bloch oscillations for torsional wavespropagating in chirped mechanical beams. After extensive simulations, threequasi-one-dimensional chirped structures were designed, constructed andexperimentally characterized by Doppler spectroscopy. When the chirp intensityvanishes a perfect periodic system, with bands and gaps, is obtained. Themechanical rainbow trapping effect occurs for small values of the chirpintensity. The wave packet traveling along the beam is progressively slowingdown and is reflected back at a certain depth, which depends on its centralfrequency. In this case a new kind of oscillation, here named "{\em rectifiedrainbow-Bloch oscillation}", appears since the wave packet is reflected at oneside by the interface between the structure and the uniform rod and by theminigap at the opposite side. For larger values of the chirp parameter therainbow trapping yields the penetration length where the mechanical Blochoscillations emerge. Numerical simulations based on the transfer matrix methodare in agreement with experimental data.

Mechanical Rainbow Trapping and Bloch Oscillations in Structured Elastic Beams