Elastic waves in phononic monolayer granular membranes

Tournat, Vincent; Pérez‐Arjona, Isabel; Merkel, Aurélien; Sánchez‐Morcillo, Víctor J.; Gusev, Vitalyi

doi:10.1088/1367-2630/13/7/073042

Cited by 27 publications

(35 citation statements)

References 42 publications

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“…However, there is an important difference, as vibrations of a granular monolayer involve rotations of the spheres [10,12]. Spheres also have internal mechanical degrees of freedom; consequently, in addition to contact-based modes, one would expect to see collective modes originating from spheroidal vibrations of the spheres [13].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Vibrational dynamics of a two-dimensional microgranular crystal

et al. 2017

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“…Several recent studies have demonstrated, in both theoretical [16,17] and experimental [18] contexts, that the rotational degree of freedom has a profound effect on the dynamics of ordered granular media. In particular, the study of Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the study of Ref. [16] focused on the dynamics of granular monolayers (whereas Refs. [17,18] explored bulk granular structures), including cases involving interaction between the monolayer and a substrate.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a monolayer of microspheres on an elastic substrate

2015

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We present a model for wave propagation in a monolayer of spheres on an elastic substrate. The model, which considers sagittally polarized waves, includes: horizontal, vertical, and rotational degrees of freedom; normal and shear coupling between the spheres and substrate, as well as between adjacent spheres; and the effects of wave propagation in the elastic substrate. For a monolayer of interacting spheres, we find three contact resonances, whose frequencies are given by simple closedform expressions. For a monolayer of isolated spheres, only two resonances are present. The contact resonances couple to surface acoustic waves in the substrate, leading to mode hybridization and "avoided crossing" phenomena. We present dispersion curves for a monolayer of silica microspheres on a silica substrate, assuming adhesive Hertzian interactions, and compare calculations using an effective medium approximation (including elasticity of the substrate) to a discrete model of a monolayer on a rigid substrate. While the effective medium model does not describe discrete lattice effects occurring at short wavelengths, we find that it is well suited for describing the interaction between the monolayer and substrate in the long wavelength limit. We suggest that a complete picture of the dynamics of a monolayer adhered to an elastic substrate can be found by combining the dispersion curves generated with the effective medium model for the elastic substrate and with the discrete model for the rigid substrate. This model is potentially scalable for use with nano-to macroscale systems, and offers the prospect of experimentally extracting contact stiffnesses from measurements of acoustic dispersion.

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“…Coupled rotational-translational elastic waves were observed in three-dimensional, hexagonal closely-packed granular crystals 16 , the dispersion relation of which is decribed by a three-dimensional discrete lattice model that includes the rotational degrees of freedom. Moreover, a twodimensional discrete lattice model, with particles possessing one translational and two rotational degrees of freedom, has been applied to a monolayer granular phononic membrane 17 . The significance of micro rotations has also been recently revealed experimentally in colloidal-based metamaterials 18 as well as in torsional waves within granular chains 19 .…”

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confidence: 99%

Tunable magneto-granular phononic crystals

Allein

Tournat

Gusev

et al. 2016

Applied Physics Letters

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This paper reports on the study of the dynamics of 1D magneto-granular phononic crystals composed of a chain of spherical steel beads inside a properly designed magnetic field. This field is induced by an array of permanent magnets, located in a holder at a given distance from the chain. The theoretical and experimental results of the band gap structure are displayed, including all six degrees of freedom for the beads, i.e. three translations and three rotations. Experimental evidence of transverse-rotational modes of propagation is presented; moreover, by changing the strength of the magnetic field, the dynamic response of the granular chain is tuned. The combination of non-contact tunability with the potentially strong nonlinear behavior of granular systems ensures the suitability of magneto-granular phononic crystals as nonlinear, tunable mechanical metamaterials for use in controlling elastic wave propagation.The ability to control the propagation of elastic waves has been widely investigated in phononic crystals, which are a class of engineered media composed of periodic arrays of scattering inclusions in a homogeneous host material 1 . The propagation of sound in phononic crystals is driven by the interference between Bragg scattered waves. Similar to the electronic band structure of semiconductors and the electromagnetic band structure of photonic crystals, the phononic crystal structure does not allow certain frequency ranges to propagate within it. The existence of these forbidden bands makes phononic crystals suitable for direct applications, such as mechanical frequency filtering and sound insulation. In addition, the removal of inclusions along some pathways produces acoustic waveguides, demultiplexers and other elastic wave devices. To foresee the next generation of elastic devices, it would be necessary to introduce a certain degree of frequency tunability in the phononic properties. Greater interest has been shown along these lines over the last few years, and many solutions have been proposed by a number of authors; these include geometric changes to the structure by applying external stresses 2 and changes to the elastic characteristics of the constitutive materials through application of external stimuli, like an electric field 3 , temperature changes 4 or a magnetic field 5 . Among the various proposed phononic crystals, granular crystals 6 , which are closely-packed ordered arrangements of elastic particles (mainly spheres) in contact, have been the topic of a large body of recent work. Due to the Hertzian contact interaction between particles 7 , the dynamic vibration response of these structures may be nonlinear and tunable. These features make granular chains a perfect medium for studying fundamental wave structures, including solitary waves with a highly localized waveform 8,9 or discrete breathers 10 , as well as in engineering applications, e.g. tunable vibration filters 11 , impulse energy protectors 12 , acoustic lenses 13 , acoustic rectifiers 14 , tunable functional switches 15 . Pr...

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Elastic waves in phononic monolayer granular membranes

Cited by 27 publications

References 42 publications

Vibrational dynamics of a two-dimensional microgranular crystal

Vibrational dynamics of a two-dimensional microgranular crystal

Dynamics of a monolayer of microspheres on an elastic substrate

Tunable magneto-granular phononic crystals

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