Experimental Evidence of Rainbow Trapping and Bloch Oscillations of Torsional Waves in Chirped Metallic Beams.

The Bloch oscillations (BO) and the rainbow trapping (RT) are two apparently unrelated phenomena, the former arising in solid state physics and the latter in metamaterials. A Bloch oscillation, on the one hand, is a counter-intuitive effect in which electrons start to oscillate in a crystalline structure when a static electric field is applied. This effect has been observed not only in solid state physics but also in optical and acoustical structured systems since a static electric field can be mimicked by a chirped structure. The RT, on the other hand, is a phenomenon in which the speed of a wave packet is slowed down in a dielectric structure; different colors then arrive to different depths within the structure thus separating the colors also in time. Here we show experimentally the emergence of both phenomena studying the propagation of torsional waves in chirped metallic beams. Experiments are performed in three aluminum beams in which different structures were machined: one periodic and two chirped. For the smaller value of the chirping parameter the wave packets, with different central frequencies, are back-scattered at different positions inside the corrugated beam; the packets with higher central frequencies being the ones with larger penetration depths. This behavior represents the mechanical analogue of the rainbow trapping effect. This phenomenon is the precursor of the mechanical Bloch oscillations, which are here demonstrated for a larger value of the chirping parameter. It is observed that the oscillatory behavior observed at small values of the chirp parameter is rectified according to the penetration length of the wave packet.

Scattering of flexural waves from a hole in a thin plate with an internal beam.

The scattering of flexural waves by a hole in a thin plate traversed by a beam is modeled here by coupling the Kirchhoff-Love and the Euler-Bernoulli theories. A closed form expression is obtained for the transfer matrix (T-matrix) relating the incident wave to the scattered cylindrical waves. For this purpose, a general method has been developed, based on an analogous impedance method for acoustic waves, for calculating the T-matrix for flexural wave scattering problems. The T-matrix for the problem considered displays a simple structure, composed of distinct sub-matrices which decouple the inside and the outside fields. The conservation of energy principle and numerical comparisons with a commercial finite element simulator have been used to prove the theory.

Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere.

This Letter presents the design, fabrication, and experimental characterization of a directional three-dimensional acoustic cloak for airborne sound. The cloak consists of 60 concentric acoustically rigid tori surrounding the cloaked object, a sphere of radius 4 cm. The major radii and positions of the tori along the symmetry axis are determined using the condition of complete cancellation of the acoustic field scattered from the sphere. They are obtained through an optimization technique that combines genetic algorithm and simulated annealing. The scattering cross section of the sphere with the cloak, which is the magnitude that is minimized, is calculated using the method of fundamental solutions. The low-loss fabricated cloak shows a reduction of the 90% of the sphere scattering cross section at the frequency of 8.55 kHz.