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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01 Apr 2016
TL;DR: In this article, the influence of disorder on energy and momentum transport, the sound wave speed and its low-pass frequency-filtering characteristics is the subject of the study. And the connection between the particle-microscale disorder and dynamics and the system-macroscale wave propagation, which can be applied to nondestructive testing, seismic exploration of buried objects (oil, mineral, etc.) or to study the internal structure of the Earth.
Abstract: . Disorder of size (polydispersity) and mass of discrete elements or particles in randomly structured media (e.g., granular matter such as soil) has numerous effects on the materials' sound propagation characteristics. The influence of disorder on energy and momentum transport, the sound wave speed and its low-pass frequency-filtering characteristics is the subject of this study. The goal is understanding the connection between the particle-microscale disorder and dynamics and the system-macroscale wave propagation, which can be applied to nondestructive testing, seismic exploration of buried objects (oil, mineral, etc.) or to study the internal structure of the Earth. To isolate the longitudinal P-wave mode from shear and rotational modes, a one-dimensional system of equally sized elements or particles is used to study the effect of mass disorder alone via (direct and/or ensemble averaged) real time signals, signals in Fourier space, energy and dispersion curves. Increase in mass disorder (where disorder has been defined such that it is independent of the shape of the probability distribution of masses) decreases the sound wave speed along a granular chain. Energies associated with the eigenmodes can be used to obtain better quality dispersion relations for disordered chains; these dispersion relations confirm the decrease in pass frequency and wave speed with increasing disorder acting opposite to the wave acceleration close to the source.
17 citations
TL;DR: In this paper, the authors numerically studied nonlinear pulse propagation in a two-dimensional (2D) granular channel composed of a main homogeneous lattice with several pairs of side granules and showed that by simply changing the direction of pulse transmission it is possible to switch the nonlinear acoustics from Nesterenko solitary pulses to strongly decaying propagating pulses.
Abstract: Granular media composed of ordered arrays of discrete spherical granules have attracted considerable attention due to their highly nonlinear and discontinuous dynamics and acoustics that enable passively adaptive and tailorable properties. In this work we numerically study nonlinear pulse propagation in a two-dimensional (2D) granular channel composed of a main homogeneous lattice with several pairs of side granules. Depending on the direction of pulse transmission in the main lattice, a periodic series of symmetry-breaking clearances alter the topology of this 2D granular network. The rotational dynamics of the individual granules, as well as dissipative effects due to friction between granules (and their boundaries) and inherent material damping, are proven to play a significant role in the acoustics of the granular channel. This is demonstrated by comparing the theoretical predictions of this work to experimental measurements of the same system reported earlier. Moreover, the strong nonlinearity of this system in synergy with the topological asymmetry introduced by the clearances passively breaks acoustic reciprocity. To this end, a detailed study of pulse transmission in the 2D granular channel is performed, and it is shown that by simply changing the direction of pulse transmission it is possible to switch the nonlinear acoustics from Nesterenko solitary pulses to strongly decaying propagating pulses. In the latter case there is continuous and irreversible transfer of energy from the main propagating pulse to the side granules, which act, in essence, as nonlinear energy absorbers. This work highlights the important role that (even small) geometric imperfections (asymmetries) may play on the acoustics of 2D granular media.
17 citations
TL;DR: In this article, a comparative evaluation of the dissipative normal nonlinear Hertz type contact, extensively explored in the discrete element simulations, is addressed, and the contribution of models to the propagation of force in a chain of contacting particles is demonstrated.
16 citations
TL;DR: In this paper, the effects of particle size, wave travel distance, confining pressure, void ratio, and adopted damping methods on the output frequency and calculated shear wave velocity are systematically analyzed.
16 citations
Posted Content•
TL;DR: In this article, a mixed numerical/analytical correction algorithm was developed to estimate the velocity of the particles during pulse propagation, which is in turn able to correctly predict the momentum and kinetic energy along the chain for several tapering configurations.
Abstract: We study momentum and energy propagation in 1D tapered chains of spherical granules which interact according to a Hertz potential. In this work we apply the binary collision approximation, which is based on the assumption that transfer of energy along the chain occurs via a succession of two-particle collisions. Although the binary theory correctly captures the trends of increase or decrease of kinetic energy and momentum, the actual values of these quantities are not in good quantitative agreement with those obtained by numerically integrating the full equations of motion. To address this difficulty we have developed a mixed numerical/analytical correction algorithm to provide an improved estimate of the velocity of the particles during pulse propagation. With this corrected velocity we are in turn able to correctly predict the momentum and kinetic energy along the chain for several tapering configurations, specifically for forward linear, forward exponential, backward linear and backward exponential tapering.
14 citations
References
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01 Jan 1934
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.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
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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.
Abstract: This paper presents a simple model for such processes as spin diffusion or conduction in the "impurity band." These processes involve 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. In this simple model the essential randomness is introduced by requiring the energy to vary randomly from site to site. It is shown that at low enough densities no diffusion at all can take place, and the criteria for transport to occur are given.
9,647 citations
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01 Jan 1951
TL;DR: The equilibrium of rods and plates Elastic waves Dislocations Thermal conduction and viscosity in solids Mechanics of liquid crystals Index as discussed by the authors The equilibrium of rod and plate elastic waves Elastic waves
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TL;DR: In this paper, the authors present a list of superconductivity properties of solids with respect to periodic structure, lattice wave properties, electron states, and electron-electron interaction.
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