Breathers in a locally resonant granular chain with precompression

Liu, Lifeng; James, Guillaume; Kevrekidis, P. G.; Vainchtein, Anna

doi:10.1016/j.physd.2016.05.007

Cited by 30 publications

(23 citation statements)

References 42 publications

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“…To find breathers in a magnetic chain, one can alternatively use a lattice with spatial heterogeneity (e.g. a dimer) [43][44][45] or one with an on-site potential [46,47] or local resonators [48,49]. The right boundary (n=12) is fixed, and the left boundary (n=−12) is driven harmonically with an electrodynamic transducer.…”

Section: Theoretical Setupmentioning

confidence: 99%

Nonlinear excitations in magnetic lattices with long-range interactions

et al. 2019

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We study-experimentally, theoretically, and numerically-nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with algebraically-decaying interactions. It was established two decades ago (Flach 1998 Phys. Rev. E 58 R4116) that lattices with long-range interactions can have breather solutions in which the spatial decay of the tails has a crossover from exponential to algebraic decay. In this article, we revisit this problem in the setting of a chain of repelling magnets with a mass defect and verify, both numerically and experimentally, the existence of breathers with such a crossover.

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Section: Theoretical Setupmentioning

confidence: 99%

Nonlinear excitations in magnetic lattices with long-range interactions

et al. 2019

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“…(27) and Fig. 6) [120,121]. In the presence of precompression, [121] examined (i) traveling bright breathers and (ii) stationary and traveling dark breathers.…”

Section: Breather Variants In Homogeneous Chain Configurationsmentioning

confidence: 99%

Nonlinear coherent structures in granular crystals

Chong

Porter

Kevrekidis

et al. 2017

J. Phys.: Condens. Matter

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The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals, a type of nonlinear metamaterial, exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures -which include traveling solitary waves, dispersive shock waves, and discrete breathers -have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

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“…We now seek traveling waves of speed c to the dynamical equations in the form ∆ i (t) = R(i−ct) and d i (t) = S(i−ct), substituting these expressions in (33) and (34). The resulting advance-delay differential equations in the traveling wave variable ξ = i − ct are then of the form:…”

Section: A the Pego-english Approach And The Existence Of Nanopteramentioning

confidence: 99%

Wave propagation in a strongly nonlinear locally resonant granular crystal

Vorotnikov

Starosvetsky

Theocharis

et al. 2018

Physica D: Nonlinear Phenomena

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In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.

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Breathers in a locally resonant granular chain with precompression

Cited by 30 publications

References 42 publications

Nonlinear excitations in magnetic lattices with long-range interactions

Nonlinear excitations in magnetic lattices with long-range interactions

Nonlinear coherent structures in granular crystals

Wave propagation in a strongly nonlinear locally resonant granular crystal

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