On the wave propagation analysis and supratransmission prediction of a
  metastable modular metastructure for non-reciprocal energy transmission

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Abstract

In this research, we investigate the nonlinear energy transmission phenomenon in a metastable modular metastructure. Numerical studies on a 1D metastable chain demonstrates that when driving frequency is within the stopband of the periodic structure, there exists a threshold for the input amplitude, beyond which sudden increase in the energy transmission can be observed. This onset of transmission is due to nonlinear instability and is known as supratransmission. We show that due to spatial asymmetry of strategically configured constituents, such transmission thresholds could shift considerably when structure is excited from different ends and therefore enabling the non-reciprocal energy transmission. We demonstrate that the critical threshold amplitude can be predicted analytically using a localized nonlinear-linear model combining harmonic balancing and transfer matrix analyses. These investigations elucidate the rich and intricate dynamics achievable by nonlinearity, asymmetry, and metastability, and provide new insights and opportunities to accomplish non-reciprocal wave energy transmissions.

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Sound isolation and giant linear nonreciprocity in a compact acoustic circulator.

Romain Fleury, Dimitrios L Sounas, Caleb Sieck … (2014)

Acoustic isolation and nonreciprocal sound transmission are highly desirable in many practical scenarios. They may be realized with nonlinear or magneto-acoustic effects, but only at the price of high power levels and impractically large volumes. In contrast, nonreciprocal electromagnetic propagation is commonly achieved based on the Zeeman effect, or modal splitting in ferromagnetic atoms induced by a magnetic bias. Here, we introduce the acoustic analog of this phenomenon in a subwavelength meta-atom consisting of a resonant ring cavity biased by a circulating fluid. The resulting angular momentum bias splits the ring's azimuthal resonant modes, producing giant acoustic nonreciprocity in a compact device. We applied this concept to build a linear, magnetic-free circulator for airborne sound waves, observing up to 40-decibel nonreciprocal isolation at audible frequencies.

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Bifurcation-based acoustic switching and rectification.

N Boechler, G. Theocharis, C. Daraio (2011)

Switches and rectification devices are fundamental components used for controlling the flow of energy in numerous applications. Thermal and acoustic rectifiers have been proposed for use in biomedical ultrasound applications, thermal computers, energy- saving and -harvesting materials, and direction-dependent insulating materials. In all these systems the transition between transmission states is smooth with increasing signal amplitudes. This limits their effectiveness as switching and logic devices, and reduces their sensitivity to external conditions as sensors. Here we overcome these limitations by demonstrating a new mechanism for tunable rectification that uses bifurcations and chaos. This mechanism has a sharp transition between states, which can lead to phononic switching and sensing. We present an experimental demonstration of this mechanism, applied in a mechanical energy rectifier operating at variable sonic frequencies. The rectifier is a granular crystal, composed of a statically compressed one-dimensional array of particles in contact, containing a light mass defect near a boundary. As a result of the defect, vibrations at selected frequencies cause bifurcations and a subsequent jump to quasiperiodic and chaotic states with broadband frequency content. We use this combination of frequency filtering and asymmetrically excited bifurcations to obtain rectification ratios greater than 10(4). We envisage this mechanism to enable the design of advanced photonic, thermal and acoustic materials and devices.