Frequency filtering in disordered granular chains
TL;DR: In this article, disorder-induced frequency filtering is studied for one-dimensional systems composed of random, pre-stressed masses interacting through both linear and nonlinear (Hertzian) repulsive forces.
Abstract: The study of disorder-induced frequency filtering is presented for one-dimensional systems composed of random, pre-stressed masses interacting through both linear and nonlinear (Hertzian) repulsive forces. An ensemble of such systems is driven at a specified frequency, and the spectral content of the propagated disturbance is examined as a function of distance from the source. It is shown that the transmitted signal contains only low-frequency components, and the attenuation is dependent on the magnitude of disorder, the input frequency, and the contact model. It is found that increased disorder leads to a narrower bandwidth of transmitted frequencies at a given distance from the source and that lower input frequencies exhibit less sensitivity to the arrangement of the masses. Comparison of the nonlinear and linear contact models reveals qualitatively similar filtering behavior; however, it is observed that the nonlinear chain produces transmission spectrums with a greater density at the lowest frequencies. In addition, it is shown that random masses sampled from normal, uniform, and binary distributions produce quantitatively indistinguishable filtering behavior, suggesting that knowledge of only the distribution’s first two moments is sufficient to characterize the bulk signal transmission behavior. Finally, we examine the wave number evolution of random chains constrained to move between fixed end-particles and present a transfer matrix theory in wave number space, and an argument for the observed filtering based on the spatial localization of the higher-frequency normal modes.
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TL;DR: In this article , the role of the finer particles in stress-strain response, liquefaction resistance and internal stability of non-cohesive gap-graded soils is quantified using laboratory geophysics.
Abstract: The behaviour of gap-graded granular materials – that is, mixtures of coarse and cohesionless finer grains with measurable differences in particle size – does not always conform to established frameworks of sand behaviour. Prior research has revealed that the role of the finer particles on the stress–strain response, liquefaction resistance and internal stability of non-cohesive gap-graded soils is significant and complex, and highly dependent on both the volumetric proportion of finer particles in the material and the size ratio of coarse particles to finer particles. Quantifying the participation of the finer particles in stress transmission and overall behaviour is central to understanding the behaviour of these materials. No experimental technique for directly quantifying the contribution of finer particles to the overall behaviour, however, has hitherto been proposed. This paper explores to what extent the participation of finer particles can be assessed using laboratory geophysics, recognising that granular materials act as a filter to remove the high-frequency components of applied seismic/sound waves. Discrete-element method simulations are performed to understand the link between particle-scale stress transmission and the overall response observed during shear wave propagation. When the proportion of finer particles is increased systematically, both the shear wave velocity (V S ) and low-pass frequency (f lp ) increase sharply once a significant amount of the applied stress has been transferred by way of the finer particles. This trend is also observed in equivalent laboratory experiments. Consequently, the f lp –V S relationship can provide useful insights to assess whether the finer particles contribute to stress transmission and hence the mechanical behaviour of gap-graded materials.
13 citations
TL;DR: In this paper, the dynamics of highly polydisperse finite granular chains are investigated, and the authors identify which particular single-particle displacements lead to energy localization from the spatiospectral properties of small vibrations, and address a fundamental question: Do granular nonlinearities and the resulting chaotic dynamics destroy this energy localization?
Abstract: We investigate the dynamics of highly polydisperse finite granular chains. From the spatiospectral properties of small vibrations, we identify which particular single-particle displacements lead to energy localization. Then, we address a fundamental question: Do granular nonlinearities and the resulting chaotic dynamics destroy this energy localization? Our numerical simulations show that for moderate nonlinearities, the overall system behaves chaotically, and spreading of energy occurs. However, long-lasting chaotic energy localization is observed for particular single-particle excitations in the presence of the nonsmooth nonlinearities. On the other hand, for sufficiently strong nonlinearities, the granular chain reaches energy equipartition. In this case, an equilibrium chaotic state is reached independent of the initial position excitation.
13 citations
01 Aug 2013
TL;DR: Acknowledgements and acknowledgements are given in this paper, along with a list of figures, tables, and lists of tables, including tables and figures, for each of the following categories:
Abstract: ..................................................................................................................................... 5 Acknowledgements .................................................................................................................... 6 List of Figures .......................................................................................................................... 13 List of Tables ........................................................................................................................... 41
11 citations
Cites background or methods or result from "Frequency filtering in disordered g..."
...By comparing the plots for transmitted and received signals the effect of frequency filtering in a granular system was clearly observed as previously noted by Zhu et al. (1996) and Lawney & Luding (2013)....
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...The higher velocity components coincided with higher frequency waves so this indicated that the sample was acting as a frequency filter similar to the samples explored by Lawney & Luding (2013) and mentioned in Chapter 2....
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...This frequency filtering was observed on a one-dimensional chain of particles in numerical simulations carried out by Lawney & Luding (2013) and in experimental work carried out by Zhu et al. (1996) using photoelastic disks....
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...For nondispersive systems the value of group velocity equals the value of phase velocity but even one-dimensional chains of particles were seen to behave in a dispersive nature in Lawney & Luding (2013)....
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...Using an analytical approach, Lawney & Luding (2013) further investigated the observation of frequency filtering in a one-dimensional chain of particles....
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TL;DR: In this article, the incoherent transport of ultrasound waves in water-saturated sintered glass bead packings is experimentally investigated, and the spectral energy density of scattered high-frequency waves is explained by a diffusion wave equation.
Abstract: The incoherent transport of ultrasound waves in water-saturated sintered glass bead packings is experimentally investigated. The spectral energy density of scattered high-frequency waves is explained by a diffusion wave equation. Immersion broadband transducers with central frequencies of 1 MHz are positioned at a distance of 73 mm to the porous sample. The diffusion coefficient and quality factor are predicted from a diffusion approximation of the time-dependent intensity curve to the ensemble-averaged measurement data. From the diffusion coefficient, we deduce a mean-free path for scattering events at lz - 0:87 60:03 mm close to the range of particle diameters of the samples (1:0 < dp < 1:2 mm). Results are in good agreement with observations from Jia (2004, "Codalike Multiple Scattering of Elastic Waves in Dense Granular Media," Phys. Rev. Lett., 93(15), p. 154303) observed for nonsintered and consolidated bead packings (0:6 < dp < 0:8 mm). The low-quality factor Q = 190 ± 10 indicates a high amount of intrinsic damping of the scattered waves although water was used as saturating and coupling fluid.
10 citations
TL;DR: In this article, the authors studied nonlinear scattering of impeding pulses at the interface of an impulsively excited dimer chain with a dispersive elastic boundary, namely, a finite linear string resting on an elastic foundation.
Abstract: Uncompressed granular dimer chains composed of repetitive pairs of heavy-light spherical, linearly elastic beads exhibit interesting intrinsic responses. The dynamics of these highly discontinuous nonlinear media is governed by the mass ratio scaling the mass disparity of each heavy-light pair of beads. In particular, it has been theoretically and experimentally shown that they support countable infinities of anti-resonances at a discrete set of mass ratios leading to solitary pulses propagating through the dimers with no attenuation or distortion. Conversely, they support countable infinities of resonances at a different discrete set of mass ratios, leading to substantial and rapid attenuation of propagating pulses due to energy scattering from low-to-high frequencies and wavenumbers by means of radiating traveling waves. In this work we computationally study nonlinear scattering of impeding pulses at the interface of an impulsively excited dimer chain with a dispersive elastic boundary, namely, a finite linear string resting on an elastic foundation. We develop a computational algorithm which, through iteration and interpolation at successive time steps, accurately computes (and ensures convergence of) the highly discontinuous contact forces and displacements at the flexible interface of the granular medium. This enables accurate computation of wave transmission, reflection, localization or multi-scale nonlinear scattering at the flexible interface for varying mass ratios of the dimer and the interface parameters. We show that, depending on the mass ratio of the dimer and the stiffness of the elastic foundation, the nonlinear scattering at the flexible interface may lead to significant reduction of the maximum contact force at the interface, and, thus, drastically affect the transmitted and reflected energy at the flexible boundary. In fact, an inverse relation between the stiffness of the elastic foundation and the residual energy transferred from the dimer chain to the flexible boundary is found. Moreover, for sufficiently small mass ratios of the dimer chain transient breathers are realized close to the interface in the form of localized “fast” oscillations of light granules of the dimer that entrap shock energy and then release in a slow time scale back to the chain and the flexible boundary. This work paves the way for studying highly discontinuous and nonlinear scattering phenomena at interfaces of granular media with flexible continua.
10 citations
References
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TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
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TL;DR: In this article, a simple model for spin diffusion or conduction in the "impurity band" is presented, which involves transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites.
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9,647 citations
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