Topologically protected waves in classical media provide unique opportunities for one-way wave transport and immunity to defects. Contrary to acoustics and electromagnetics, their observation in elastic solids has so far been elusive because of the presence of multiple modes and their tendency to hybridize at interfaces. Here, we report on the experimental investigation of topologically protected helical edge modes in elastic plates patterned with an array of triangular holes, along with circular holes that produce an accidental degeneracy of two Dirac cones. Such a degeneracy is subsequently lifted by careful breaking of the symmetry along the thickness direction, which emulates the spin orbital coupling in the quantum spin Hall effect. The joining of two plates that are mirror-symmetric copies of each other about the plate midthickness introduces a nontrivial interface that supports helical edge waves. The experimental observation of these topologically protected wave modes in elastic continuous plates opens avenues for the practical realization of structural components with topologically nontrivial waveguiding properties and their application to elastic waveguiding and confinement.
The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome digital signal processing techniques. Here, we propose and experimentally validate an alternative approach, using the filtering and focusing properties of phononic crystals to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and damage detection. DOI: 10.1103/PhysRevLett.118.214301 In recent years, phononic crystals (PCs) have attracted great attention due to their unconventional dynamic behavior, with effects such as negative refraction [1], frequency band gaps [2,3], wave filtering or focusing [4][5][6], acoustic cloaking [7][8][9], subwavelength sensing [10,11], etc. Their periodic structure, rather than single material constituents, is responsible for their behavior, which exploits Bragg scattering [12,13]. Their attractive properties to act as stopband filters [12] or to concentrate energy in selected frequency ranges [14] makes them potentially interesting for nonlinear elastic source detection and to reveal the presence of defects, e.g. cracks, in a sample. This is because, in general, a nonlinear response is generated at the defect location and several possible features may appear, including the generation of higher order harmonics [15][16][17] or subharmonics [18,19], the nonlinear dependence of the elastic modulus and of attenuation coefficients on strain [20][21][22], and, as a consequence, the shift of the resonance frequency with increasing excitation amplitude [23,24] and the failure of the superposition principle [25,26]. All of these possible signatures can be used to detect and monitor the presence and evolution of damage, exploiting the greater sensitivity of nonlinear detection techniques compared to conventional linear ones [27].In the past years, nonlinear imaging techniques such as b scan, c scan, and tomography [28] have attracted much interest. A particularly robust and efficient approach is the combination of time reversal (TR) and nonlinear elastic wave spectroscopy (NEWS). This technique (TR-NEWS) exploits space-time focusing of the wave field achieved in TR [29] and applies it to a defect acting as a source of nonlinear elastic waves [30][31][32][33]. The scattered signal is recorded, the frequency generated by the primary source is filtered out using a bandpass filter, and the resulting signal is time reversed and reinjected by the receiver: due to the (t → −t) symmetry, the wave field back propagates to its original (nonlinear) source, focusing energy at the defect location at a specific time. Many studies have proved the efficiency and robustness of TR-NEWS in various configurations, for ...
Large tuned air‐gun arrays operated in off‐shore petroleum exploration are also used for deep penetration marine seismic reflection surveys conducted to define structures in the earth’s crust. Because of the attenuation of higher frequencies, the useful upper frequency limit of these records is usually about 50–60 Hz. The aim of this paper is to report on a method of seismic pulse generation that preferentially concentrates the air gun’s energy in the low range of the seismic frequency band by centering the output on the first “bubble pulse” instead of the initial (primary) pulse. Experimental results show that, due to the increased low‐frequency energy content of this “single bubble” pulse, air‐gun arrays considerably reduced both in size and volume can generate the necessary acoustic energy for deep seismic exploration.
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