Experimental Evidence of Rotational Elastic Waves in Granular Phononic Crystals

Merkel, Aurélien; Tournat, Vincent; Gusev, Vitalyi

doi:10.1103/physrevlett.107.225502

Cited by 118 publications

(105 citation statements)

References 26 publications

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“…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%

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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“…26 Experimental observation of coupled rotational-translational modes in 3D, hexagonal closely packed granular phononic crystals has been recently carried out. 27 Experimental evidence of transverse rotational modes has also been observed in a 1D magnetogranular phononic crystal, with beads of 15.875 mm diameter. 28 Effects of nonlinear dynamic hysteresis, such as nonlinear absorption, have been shown to occur in granular chains under torsional excitation.…”

Section: A Granular Chain Terminated By a Rigid Support: Fea Resultsmentioning

confidence: 85%

The dynamic excitation of a granular chain: Contact mechanics finite element analysis and experimental validation

Gélat

Yang

Akanji

et al. 2017

The Journal of the Acoustical Society of America

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There is currently interest in transmitting acoustic signals along granular chains to produce waveforms of relevance to biomedical ultrasound applications. The study of such a transduction mechanism is greatly aided by the use of validated theoretical models. In view of this, a finite element analysis is presented in this paper. The dynamics of a granular chain of six, 1 mm diameter chrome steel spherical beads, was excited at one end using a sinusoidal displacement signal at 73 kHz, and terminated by a rigid support. Output from this model was compared with the solution provided by the equivalent discrete dynamics model, and good agreement obtained. An experimental configuration involving the same chain, but terminated by an annular support made of a liquid photopolymer resin was also simulated and the velocity of the last sphere obtained through simulation was compared with laser vibrometer measurement, with good agreement. This model was then extended whereby the granular chain was coupled to an acoustic medium with the properties of water, via a thin vitreous carbon cylinder. Finite element predictions of the acoustic pressure indicate that, for a 73 kHz excitation frequency, harmonic rich acoustic pulses with harmonic content close to 1 MHz are predicted.

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“…More recently, Sadovskaya, 2010, andSadovskii, 2015, analyzed the propagation of waves in blocky materials modeled as an equivalent orthotropic Cosserat continuum. Finally, it is worth noting that Merkel et al, 2011, have highlighted some limitations of the Cosserat model in simulating the optical band structure of hexagonally packed granular materials in the neighborhood of long waves. In particular, these Authors criticized the inability of the Cosserat model to simulate the downward concavity of the optical branch in the Bloch domain obtained in the Lagrangian model for long rotational wavelengths.…”

Section: Introductionmentioning

confidence: 99%

“…Some numerical examples are analyzed to appreciate both the influence of the model parameters on the band structure and to assess the validity limits of the Cosserat continuum. This investigation is also aimed at understanding and solving the mentioned criticism by Merkel et al, 2011, regarding the capability of the Cosserat model to approximate the optical branch. Although the 5 present formulation provides a constitutive model that in several cases is characterized by negative definiteness of the elastic tensor of the microcurvatures, however, the existence and uniqueness of the solution of the dynamic problems considered in the examples has been verified through the ellipticity condition of Legendre-Hadamard, namely by verifying that the wave phase velocity in the elastic micropolar continuum is real.…”

Section: Introductionmentioning

confidence: 99%

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

Bacigalupo

Gambarotta

2017

Journal of the Mechanics and Physics of Solids

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Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected each other through homogeneous linear interfaces, have been analysed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet-Bloch approach. From the resulting eigenproblem derived by the Euler-Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results has been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analysed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, it appears that the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of the block. Finally, in consideration that the positive definiteness of the second order elastic tensor of the micropolar model is not guaranteed, the hyperbolicity of the equation of motion has been investigated by considering the Legendre-Hadamard ellipticity conditions requiring real values for the wave velocity.

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Experimental Evidence of Rotational Elastic Waves in Granular Phononic Crystals

Cited by 118 publications

References 26 publications

Vibrational dynamics of a two-dimensional microgranular crystal

Vibrational dynamics of a two-dimensional microgranular crystal

The dynamic excitation of a granular chain: Contact mechanics finite element analysis and experimental validation

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

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