Nonlinear resonances and energy transfer in finite granular chains

Lydon, Joseph; Theocharis, G.; Daraio, Chiara

doi:10.1103/physreve.91.023208

Cited by 62 publications

(31 citation statements)

References 28 publications

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“…The bending trend of the resonant peaks as the driving amplitude varies is shown in Fig. 3 (see also [52]). This, in conjunction with the multimodal nature of our system, implies the possibility of high-amplitude states for a broad range of frequencies.…”

Section: Resultsmentioning

confidence: 93%

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Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains

et al. 2016

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This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multimodal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the nonlinear Schrödinger equation predicts the corresponding modes fairly well. The electromechanical model we apply predicts accurately the conversion from the obtained mechanical energy to the electrical energy observed in experiments.

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Section: Resultsmentioning

confidence: 93%

“…2(b)] or when considering a single oscillator [see, e.g., the insets in Figs. 2(a)-2(c) in [52] for the case of a single granular particle]. This is because, in the absence of the bent resonant peaks, the response will be of a low amplitude.…”

Section: Resultsmentioning

confidence: 99%

Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains

et al. 2016

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“…When acoustic waves propagate within a nonlinear acoustic medium, such as Fermi–Pasta–Ulam chains 32–34 or granular crystals 35–38 , nonlinear phenomena including discrete breathers 39 , solitons 40, 41 and bifurcations 42 can be observed. Acoustic diodes 36, 43, 44 , rectification 45 and lenses 46 based on nonlinear media have been designed.…”

Section: Introductionmentioning

confidence: 99%

Ultra-low and ultra-broad-band nonlinear acoustic metamaterials

et al. 2017

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Linear acoustic metamaterials (LAMs) are widely used to manipulate sound; however, it is challenging to obtain bandgaps with a generalized width (ratio of the bandgap width to its start frequency) >1 through linear mechanisms. Here we adopt both theoretical and experimental approaches to describe the nonlinear chaotic mechanism in both one-dimensional (1D) and two-dimensional (2D) nonlinear acoustic metamaterials (NAMs). This mechanism enables NAMs to reduce wave transmissions by as much as 20–40 dB in an ultra-low and ultra-broad band that consists of bandgaps and chaotic bands. With subwavelength cells, the generalized width reaches 21 in a 1D NAM and it goes up to 39 in a 2D NAM, which overcomes the bandwidth limit for wave suppression in current LAMs. This work enables further progress in elucidating the dynamics of NAMs and opens new avenues in double-ultra acoustic manipulation.

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“…Wave propagation in homogeneous granular chains and interactions of spherical elastic objects have been well studied both theoretically and experimentally [1][2][3][4][5]. In such a system with Hertzian contact, a nonlinear forcedeformation relation exists as F ∝ δ 1.5 .…”

Section: Introductionmentioning

confidence: 99%

“…After Nesterenko's pioneering work in 1983 [1], a great number of models were developed to simulate wave propagation in infinite and finite chains [2,4,18]. However, predicting the resonance behavior in harmonically driven monoatomic granular chains, modeling the nonlinear and dispersive effects, and minimizing the overall structure are still big challenges [5,19]. In addition to this, the problem becomes more complicated once the chain is coupled to a finite material, where a matching layer is essential for biomedical applications.…”

Section: Introductionmentioning

confidence: 99%

Generation of Ultrasound Pulses in Water Using Granular Chains with a Finite Matching Layer

et al. 2017

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Wave propagation in granular chains is subject to dispersive effects as well as nonlinear effects arising from the Hertzian contact law. This enables the formation of wideband pulses, which is a desirable feature in the context of diagnostic and therapeutic ultrasound applications. However, coupling of the ultrasonic energy from a chain of spheres into biological tissue is a big challenge. In order to improve the energy transfer efficiency into biological materials, a matching layer is required. A prototype device is designed to address this by using six aluminum spheres and a vitreous carbon matching layer. The matching layer and the precompression force are selected specifically to maximize the acoustic pressure in water and its bandwidth. The designed device generates a train of wideband ultrasonic pulses from a narrow-band input with a center frequency of 73 kHz. An analytical model is created to simulate the behavior of a matching layer as a flexible thin plate clamped from the edges. This model is then verified using free-field hydrophone measurements in water, which successfully predict the increased bandwidth by generation of harmonics. The shapes of the measured and predicted waveforms are compared by calculating the normalized cross-correlation, which shows 83% similarity between both. Since the generation of harmonics is of interest in this study, the total harmonic distortion (THD) and the −6-dB bandwidth of the signals are used to analyze signal fidelity between the hydrophone measurements and the model predictions. The acoustic signals in water have a root-mean-square THD of 73%, and the model predicts a root-mean-square THD of 78%. The −6-dB bandwidths of individual pulses measured by a hydrophone and predicted with the model are 280 and 252 kHz, respectively. At these high ultrasonic frequencies, it is an experimental demonstration of resonant chains operating in water with a matching layer.

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Nonlinear resonances and energy transfer in finite granular chains

Cited by 62 publications

References 28 publications

Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains

Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains

Ultra-low and ultra-broad-band nonlinear acoustic metamaterials

Generation of Ultrasound Pulses in Water Using Granular Chains with a Finite Matching Layer

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