Nonlinear Periodic Phononic Structures and Granular Crystals

Theocharis, G.; Boechler, Nicholas; Daraio, Chiara

doi:10.1007/978-3-642-31232-8_7

Cited by 69 publications

(83 citation statements)

References 123 publications

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“…where ρ s = 2.44 g/cm 3 , c sT = 3438 m/s, and c sL = 5711 m/s are the density, transverse, and longitudinal wave speeds of the substrate, respectively. ω 1 is the spheroidal mode frequency given by Eq.…”

Section: Spheroidal Dispersion and Interaction With Surface Rayleimentioning

confidence: 99%

“…Subsequent studies were extended to two-dimensional (2D) and three-dimensional (3D) systems and yielded an array of novel acoustic phenomena [3]. Granular crystals, as these systems became known, can be considered a class of phononic crystal [4] with unique behavior specific to granular media.…”

Section: Introductionmentioning

confidence: 99%

“…Granular crystals, as these systems became known, can be considered a class of phononic crystal [4] with unique behavior specific to granular media. For instance, in addition to nonlinear effects such as solitons and discrete breathers [2,3], unusual linear phenomena such as the existence of rotational acoustic modes have been revealed [5,6]. Due to the nonlinearity of Hertzian contacts, the acoustic properties of granular crystals can be easily tuned, for example, by applying static compression, which makes them attractive for potential applications [3].…”

Section: Introductionmentioning

confidence: 99%

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Vibrational dynamics of a two-dimensional microgranular crystal

et al. 2017

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We study the dynamics of an ordered hexagonal monolayer of polystyrene microspheres adhered to a glass substrate coated with a thin aluminum layer. A laser-induced transient grating technique is employed to generate and detect three types of acoustic modes across the entire Brillouin zone in the −K direction: low-frequency contact-based modes of the granular monolayer, high-frequency modes originating from spheroidal vibrations of the microspheres, and surface Rayleigh waves. The dispersion relation of contact-based and spheroidal modes indicates that they are collective modes of the microgranular crystal controlled by particle-particle contacts. We observe a spheroidal resonance splitting caused by the symmetry breaking due to the substrate, as well as an avoided crossing between the Rayleigh and spheroidal modes. The measurements are found to be in agreement with our analytical model.

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Section: Spheroidal Dispersion and Interaction With Surface Rayleimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibrational dynamics of a two-dimensional microgranular crystal

et al. 2017

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“…We chose a system that is well within the realm of ongoing experimental considerations, namely, a two-dimensional hexagonally packed lattice of spherical particles that interact nonlinearly through point contacts. Such systems have been termed granular crystals [23][24][25][26], and have been proposed for a range of applications including -but not limited to-shock and energy absorbing layers [27][28][29][30], actuating devices [31], acoustic lenses [32], acoustic diodes [33] and sound scramblers [34,35]. Wave propagation has been studied extensively in one-dimensional (1D) granular crystals where robust highly localized waves and variants thereof have been identified in various configurations, see the reviews [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

“…Such systems have been termed granular crystals [23][24][25][26], and have been proposed for a range of applications including -but not limited to-shock and energy absorbing layers [27][28][29][30], actuating devices [31], acoustic lenses [32], acoustic diodes [33] and sound scramblers [34,35]. Wave propagation has been studied extensively in one-dimensional (1D) granular crystals where robust highly localized waves and variants thereof have been identified in various configurations, see the reviews [23][24][25][26]. Higher dimensional granular crystals have also been studied [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], but to a far lesser extent than in 1D.…”

Section: Introductionmentioning

confidence: 99%

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

et al. 2016

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Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wavepacket, as well as via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a non-oscillatory nature, resulting from the complex interplay between the discreteness, nonlinearity and geometry of the packing. The transition between these two types of propagation is explored.

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Reprogrammable Phononic Metasurfaces

2017

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Magnetic potential and material programming We characterize the magnetic force between a 3×3 array of magnets of diameter 5 mm and thickness of 4 mm resembling the controllable magnetic field underneath the metamaterial plate. We fix the array to the forcesensing clamp in the Instron 3000 mechanical testing machine. We fix another array of 3×3 magnets to the opposite Instron clamp, 3 mm diameter and 2 mm thickness similar to the magnets embedded in the metamaterial. We start the compression test with the magnets at 15 mm distance. We move the magnet arrays close to each other and record the repulsion force in

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Nonlinear Periodic Phononic Structures and Granular Crystals

Cited by 69 publications

References 123 publications

Vibrational dynamics of a two-dimensional microgranular crystal

Vibrational dynamics of a two-dimensional microgranular crystal

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

Reprogrammable Phononic Metasurfaces

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