Scattering of Solitary Waves and Excitation of Transient Breathers in Granular Media by Light Intruders and No Precompression

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
Yuli Starosvetsky ◽  
K. R. Jayaprakash ◽  
Alexander F. Vakakis
Keyword(s):  
Granular Medium ◽  
Granular Media ◽  
Multiple Scale ◽  
Hertzian Contact ◽  
Reduced Models ◽  
Strongly Nonlinear ◽  
Granular Chains ◽  
Low Amplitude ◽  
Excitation Conditions ◽  
Nonlinear Regimes

We analyze the dynamics of strongly nonlinear granular chains of beads in Hertzian contact with light intruders. We show that the interactions of the light intruders with solitary pulses propagating through the granular medium can be approximately studied by reduced models of the intruders with only their neighboring beads under similar excitation conditions. Studying the reduced models, we identify weakly and strongly nonlinear regimes in the dynamics, depending on the degree of compression between beads and on the occurrence of separation between neighboring beads leading to collisions. We analyze weakly and strongly nonlinear oscillatory regimes of the intruder dynamics by multiple-scale analysis, and by applying special nonsmooth coordinate transformations. When separation between beads occurs, localized transient breathers are excited, corresponding to repeated collisions of an intruder with its neighbors. This leads to high-frequency scattering energy, and to radiation of energy in the granular medium in the form of low-amplitude slowly modulated oscillatory pulses. We find that repeated excitation of localized transient breathers by an array of periodically placed intruders can result in drastic reduction of the amplitude of a solitary wave propagating through the granular medium. This indicates that this type of granular media can be designed as effective shock attenuators.

scholarly journals Under pressure: Hydrogel swelling in a granular medium

2021 ◽  
Vol 7 (7) ◽  
pp. eabd2711
Author(s):  
Jean-François Louf ◽  
Nancy B. Lu ◽  
Margaret G. O’Connell ◽  
H. Jeremy Cho ◽  
Sujit S. Datta
Keyword(s):  
Oil Recovery ◽  
Granular Medium ◽  
Granular Media ◽  
Three Dimensional ◽  
Osmotic Swelling ◽  
Widespread Adoption ◽  
Dry Soil ◽  
Hydrogel Swelling

Hydrogels hold promise in agriculture as reservoirs of water in dry soil, potentially alleviating the burden of irrigation. However, confinement in soil can markedly reduce the ability of hydrogels to absorb water and swell, limiting their widespread adoption. Unfortunately, the underlying reason remains unknown. By directly visualizing the swelling of hydrogels confined in three-dimensional granular media, we demonstrate that the extent of hydrogel swelling is determined by the competition between the force exerted by the hydrogel due to osmotic swelling and the confining force transmitted by the surrounding grains. Furthermore, the medium can itself be restructured by hydrogel swelling, as set by the balance between the osmotic swelling force, the confining force, and intergrain friction. Together, our results provide quantitative principles to predict how hydrogels behave in confinement, potentially improving their use in agriculture as well as informing other applications such as oil recovery, construction, mechanobiology, and filtration.

GRANULAR MEDIA ON A VIBRATING PLATE: A MOLECULAR DYNAMICS SIMULATION

1993 ◽  
Vol 07 (09n10) ◽  
pp. 1779-1788 ◽  
Author(s):  
JASON A.C. GALLAS ◽  
HANS J. HERRMANN ◽  
STEFAN SOKOLOWSKI
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulation ◽  
Granular Materials ◽  
Granular Medium ◽  
Granular Media ◽  
Dynamics Simulation ◽  
Dissipation Of Energy ◽  
Conveyor Belts ◽  
Good Agreement ◽  
Vibrating Plate

When sand or other granular materials are shaken, poured or sheared many intriguing phenomena can be observed. We will model the granular medium by a packing of elastic spheres and simulate it via Molecular Dynamics. Dissipation of energy and shear friction at collisions are included. The onset of fluidization can be determined and is in good agreement with experiments. On a vibrating plate we observe the formation of convection cells due to walls or amplitude modulations. Density and velocity profiles on conveyor belts are measured and the influence of an obstacle discussed. We mention various types of rheology for flow down an inclined chute or through a pipe and outflowing containers.

Humidity-Induced Cohesion Effects in Granular Media

2000 ◽  
Vol 627 ◽  
Author(s):  
Nathalie Fraysse ◽  
Luc Petit
Keyword(s):  
Granular Medium ◽  
Granular Media ◽  
Global Scale ◽  
Interparticle Forces ◽  
Wetting Properties ◽  
Small Glass ◽  
Capillary Bridges ◽  
Scale Properties ◽  
Comparison Of The Results ◽  
Maximal Stability

ABSTRACTExperiments were performed under accurately-controlled humidity conditions in order to quantify effects induced by humidity on granular materials. Measurements of the maximal stability angle of a pile made of small glass beads are reported as a function of the relative vapor pressure in the cell, up to close to saturation. The comparison of the results obtained with fluids differing in their molecular interactions with glass, namely water and heptane, shows that the wetting properties of the interstitial liquid on the grains have a strong influence on the cohesion of the non-saturated granular medium. This suggests that gravimetric experiments which could indirectly give information on the size of the capillary bridges that form between grains should be useful to understand the close connection that exists, through interparticle forces, between microscopic properties such as wetting properties and surface roughness of the grains, and global-scale properties of the pile, as its stability and flowability.

Terahertz generation by tilted-front laser pulses in weakly and strongly nonlinear regimes

2013 ◽  
Vol 103 (25) ◽  
pp. 251103 ◽  
Author(s):  
Sergey B. Bodrov ◽  
Aleksey A. Murzanev ◽  
Yury A. Sergeev ◽  
Yury A. Malkov ◽  
Andrey N. Stepanov
Keyword(s):  
Laser Pulses ◽  
Terahertz Generation ◽  
Strongly Nonlinear ◽  
Nonlinear Regimes

scholarly journals Development of Approaches to Creation of Active Vibration Control System in Problems of the Dynamics for Granular Media

2018 ◽  
Vol 148 ◽  
pp. 11004 ◽  
Author(s):  
Andrei P. Khomenko ◽  
Sergey K. Kargapoltsev ◽  
Andrey V. Eliseev
Keyword(s):  
Granular Medium ◽  
Granular Media ◽  
Active Vibration Control ◽  
Evaluation Criteria ◽  
Dynamic Interactions ◽  
Theoretical Understanding ◽  
Vibration Machine ◽  
Vibration Field ◽  
Steel Balls ◽  
Analytical Approaches

The article deals with the development of mathematical models and evaluation criteria of the vibration field in the dynamic interactions of the elements of the vibrational technological machines for the processes of vibrational strengthening of long-length parts with help of a steel balls working medium. The study forms a theoretical understanding of the modes of motions of material particles in interaction with a vibrating surface of the working body of the vibration machine. The generalized approach to the assessment of the dynamic quality of the work of vibrating machines in multiple modes of tossing, when the period of free flight of particles is a multiple of the period of the surface oscillations of the working body, is developed in the article. For the correction of vibration field of the working body, the characteristics of dynamic interactions of granular elements of the medium are taken into account using original sensors. The sensors that can detect different particularities of interaction of the granular medium elements at different points of the working body are proposed to evaluate the deviation from a homogeneous and one-dimensional mode of vibration field. Specially developed sensors are able to register interactions between a single granule, a system of granules in filamentous structures, and multipoint interactions of the elements in a close-spaced cylindrical structure. The system of regularization of the structure of vibration fields based on the introduction of motion translation devices is proposed using the multi-point sensor locations on the working body. The article refers to analytical approaches of the theory of vibration displacements. For the experimental data assessment, the methods of statistical analysis are applied. It is shown that the peculiar features of the motion of granular medium registered by the sensors can be used to build active control systems of field vibration.

The Regular Pattern of Demagnetizing Factor Behaviour of Various ‘Cores’ of Granule-Ball Chains

2015 ◽  
Vol 1083 ◽  
pp. 75-79
Author(s):  
Alexander Sandulyak ◽  
Anna Sandulyak ◽  
Vera Ershova ◽  
Petr Shkatov
Keyword(s):  
Granular Medium ◽  
Granular Media ◽  
Relative Size ◽  
Regular Pattern ◽  
Magnetic Media ◽  
Full Agreement ◽  
The Core ◽  
Demagnetizing Factor ◽  
Ferro Magnetic ◽  
The One

We analyze previously not studied issue on the value, nature and manifestation f a demagnetizing factor of effective channels-magnets formed in magnetized granular media by the chains of contacting granules. We provide the factor values for conditionally defined quasi-solid cores of the channels varying in length and diameter, as well as a corresponding consolidating expression which turned out to be exponential with such an argument as the radical of the core relative size. We emphasize full agreement of this expression with the one for a granular medium, i.e. the medium consisting, basically, of the effective channels bundle according to the developed theory of channel-by-channel (selective) magnetization of granular ferro-magnetic media used, e.g. as operating elements in versatile magnetic separators.

Humidity Effects and Aging Behavior in Granular Media

1998 ◽  
Vol 543 ◽  
Author(s):  
F. Restagno ◽  
H. Gayvallet ◽  
L. Bocquet ◽  
E. Charlaix
Keyword(s):  
Relative Humidity ◽  
Granular Medium ◽  
Granular Media ◽  
Capillary Condensation ◽  
Glass Beads ◽  
Aging Behavior ◽  
Humidity Effects ◽  
Small Glass ◽  
Aging Properties ◽  
Maximum Stability

AbstractWe present a study of humidity effects on the maximum stability angle in granular media. We show that a granular medium of small glass beads exhibits aging properties: the first avalanche angle increases logarithmically with the resting time of the pile. This aging behavior is found to depend on the relative humidity of the surrounding atmosphere. A short interpretation of this effect, based on a model of activated capillary condensation, is proposed.

Tuning Methodology of Nonlinear Vibration Absorbers Coupled to Nonlinear Mechanical Systems

2011 ◽  
Author(s):  
Re´gis Viguie´ ◽  
Gae¨tan Kerschen
Keyword(s):  
Nonlinear Dynamic ◽  
Large Body ◽  
Degree Of Freedom ◽  
Primary System ◽  
Vibration Absorbers ◽  
Strongly Nonlinear ◽  
Nonlinear Mechanical ◽  
Parametric Studies ◽  
Nonlinear Mechanical Systems ◽  
Nonlinear Regimes

A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequent occurrence in engineering applications. Therefore, the present paper focuses on the mitigation of vibrations of nonlinear primary systems using nonlinear dynamic absorbers. Because most existing contributions about their design rely on extensive parametric studies, which are computationally demanding, or on analytic methods, which may be limited to small-amplitude motions, this study proposes a tuning procedure which is computationally tractable and can treat strongly nonlinear regimes of motion. The proposed methodology relies on a frequency-energy based approach followed by bifurcation analysis. The results are illustrated using a one-degree-of-freedom primary system, which can, for instance, represent the vibrations of a specific mode of a multi-degree-of-freedom structure.

Traveling and solitary waves in monodisperse and dimer granular chains

2017 ◽  
Vol 31 (10) ◽  
pp. 1742001 ◽  
Author(s):  
Yuli Starosvetsky ◽  
K. R. Jayaprakash ◽  
Alexander F. Vakakis
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Traveling Waves ◽  
Granular Media ◽  
Equations Of Motion ◽  
Continuum Approximation ◽  
Granular Chains ◽  
Solitary Pulse ◽  
Countably Infinite ◽  
Dimer Granular Chains

We provide a review of propagating traveling waves and solitary pulses in uncompressed one-dimensional ([Formula: see text]) ordered granular media. The first such solution in homogeneous granular media was discovered by Nesterenko in the form of a single-hump solitary pulse with energy-dependent profile and velocity. Considering directly the discrete, strongly nonlinear governing equations of motion of these media (i.e., without resorting to continuum approximation or homogenization), we show the existence of countably infinite families of stable multi-hump propagating traveling waves with arbitrary wavelengths. A semi-analytical approach is used to study the dependence of these waves on spatial periodicity (wavenumber) and energy, and to show that in a certain asymptotic limit, these families converge to the single-hump Nesterenko solitary wave. Then the study is extended in dimer granular chains composed of alternating “heavy” and “light” beads. For a set of specific mass ratios between the light and heavy beads, we show the existence of multi-hump solitary waves that propagate faster than the Nesterenko solitary wave in the corresponding homogeneous granular chain composed of only heavy beads. The existence of these waves has interesting implications in energy transmission in ordered granular chains.

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