Pulse propagation in decorated granular chains: An analytical approach

Harbola, Upendra; Rosas, Alexandre; Romero, Aldo H.; Esposito, Massimiliano; Lindenberg, Katja

doi:10.1103/physreve.80.051302

Cited by 47 publications

(60 citation statements)

References 36 publications

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“…In the context of the linear chain, we relate the filtering behavior to the localization of eigenmodes in the presence of disorder. One may imagine applications exploiting disorder effects, as could be pursued in the spirit of [5,10,13,14,32,40,47,49] where such systems were engineered to produce a desired output.…”

Section: Discussionmentioning

confidence: 99%

“…Additionally, there is significant attention placed on the behavior of "designed" and ordered nonlinear chains, often motivated by energy modification and shock-protection applications. Studies have employed smoothly varying mass distributions [40], "decoration" (e.g., deliberate insertion of different sized masses) [10,13,14,27] tapering [5,32,47,49] and controlled variation of the particle material [3,15]. Combinations of both tapering and decoration have also been employed [6,13].…”

Section: Introductionmentioning

confidence: 99%

“…Studies have employed smoothly varying mass distributions [40], "decoration" (e.g., deliberate insertion of different sized masses) [10,13,14,27] tapering [5,32,47,49] and controlled variation of the particle material [3,15]. Combinations of both tapering and decoration have also been employed [6,13]. The interest in non-linear, realistic wavepropagation phenomena is documented by the most recent publications on contact dissipation mechanisms in one-dimensional [31,36,38] and higher dimensional idealized granular systems [7,24,31].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Frequency filtering in disordered granular chains

Lawney¹,

Luding²

2014

Acta Mech

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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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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Frequency filtering in disordered granular chains

Lawney¹,

Luding²

2014

Acta Mech

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“…Recently, the interest to granular crystals has shifted towards periodic travelling waves as well as travelling waves in heterogeneous (dimer) chains, as more relevant for physical experiments [9,20]. Periodic wave solutions of the differential advance-delay equation were considered by James in the context of Newton's cradle [11] and homogeneous granular crystals [12].…”

Section: Introductionmentioning

confidence: 99%

Periodic Traveling Waves in Diatomic Granular Chains

Betti

Pelinovsky

2013

J Nonlinear Sci

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We study bifurcations of periodic travelling waves in granular dimer chains from the anticontinuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist.

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“…One-dimensional chains of spherical particles have been extensively studied in the literature and are known to present highly nonlinear dynamic properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. When the chains are uncompressed, they support the formation and propagation of compact solitary waves that have been predicted theoretically [1], and observed numerically [1,6] and experimentally [4,5].…”

Section: Introductionmentioning

confidence: 99%

Highly nonlinear solitary waves in chains of ellipsoidal particles

2011

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We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their propagation properties. We measure experimentally the traveling pulse amplitude (force), the solitary wave speed, and the solitary wave width. We compare these results with theoretical predictions in the long wavelength approximation, and with numerical results obtained with a discrete particle model and with finite element simulations. We also study the propagation of highly nonlinear solitary waves in the chain with particles arranged in different configurations to show the effects of the particle's geometry on the wave propagation characteristics and dissipation. We find very good agreement between experiment, theory, and simulations for all the ranges of impact velocity and particle arrangements investigated.

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Pulse propagation in decorated granular chains: An analytical approach

Cited by 47 publications

References 36 publications

Frequency filtering in disordered granular chains

Frequency filtering in disordered granular chains

Periodic Traveling Waves in Diatomic Granular Chains

Highly nonlinear solitary waves in chains of ellipsoidal particles

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