Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates

Torrent, Daniel; Mayou, Didier; Sánchez‐Dehesa, José

doi:10.1103/physrevb.87.115143

Cited by 170 publications

(165 citation statements)

References 38 publications

(41 reference statements)

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“…The mass-spring oscillator has often been used as the simplest model of a mechanical resonator on the surface of an elastic half-space [17][18][19] or a plate [20,21]. We consider the interaction of horizontal mass-spring oscillators of mass M and spring constant K on the surface z=0 of an elastically isotropic solid half-space with a shear horizontal wave propagating in the x direction and polarized in the y direction.…”

Section: Acoustic Case: Interaction Of Sh Wave In a Solid Half-spmentioning

confidence: 99%

Waveguiding by a locally resonant metasurface

Maznev

Gusev

2015

Phys. Rev. B

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Dispersion relations for acoustic and electromagnetic waves guided by resonant inclusions located at the surface of an elastic solid or an interface between two media are analyzed theoretically within the effective medium approximation. Oscillators on the surface of an elastic half-space are shown to give rise to a Love-type surface acoustic wave only existing below the oscillator frequency. A simple dispersion relation governing this system is shown to also hold for electromagnetic waves guided by Lorentz oscillators at an interface between two media with equal dielectric constants. Different kinds of behavior of the dispersion of the resonantly guided mode depending on whether the bulk wave in the absence of oscillators can propagate along the surface or interface are identified.

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Section: Acoustic Case: Interaction Of Sh Wave In a Solid Half-spmentioning

confidence: 99%

Waveguiding by a locally resonant metasurface

Maznev

Gusev

2015

Phys. Rev. B

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“…For instance, cloaking devices, [14][15][16] flat lenses based on negative refraction, 17,18 gradient index flat and circular lenses [19][20][21] and omnidirectional absorbers 22,23 for flexural waves have been recently proposed and experimentally verified. Also, the dispersion relation of plates with periodic arrangements of rigid pins, 24,25 holes, 26 attached pillars [27][28][29] or point-like spring-mass resonators [30][31][32] attached to them has been investigated by several groups, as well as the resonant properties of complex inclusions. 33 In the aforementioned works, the properties of the complex structure are mainly determined by band structure calculation, since an effective medium theory for the description of these new metamaterials, specially relating the different resonant parameters with the corresponding symmetry of the field, has not been given so far, as has been done for acoustic or bulk elastic waves.…”

Section: 13mentioning

confidence: 99%

Effective medium theory for elastic metamaterials in thin elastic plates

2014

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An effective medium theory for resonant and non-resonant metamaterials for flexural waves in thin plates is presented. The theory provides closed-form expressions for the effective mass density, rigidity and Poisson's ratio of arrangements of isotropic scatterers in thin plates, valid for low frequencies and moderate filling fractions. It is found that the effective Young's modulus and Poisson's ratio are induced by a combination of the monopolar and quadrupolar scattering coefficient, as it happens for bulk elastic waves, while the effective mass density is induced by the monopolar coefficient, contrarily as it happens for bulk elastic waves, where the effective mass density is induced by the dipolar coefficient. It is shown that resonant positive or negative effective elastic parameters are possible, being therefore the monopolar resonance the responsible of creating an effective medium with negative mass density. Several examples are given for both non-resonant and resonant effective parameters and the results are numerically verified by multiple scattering theory and finite element analysis.

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“…Thus, propagation properties of flexural waves in plates with periodic arrangements of rigid pins [1,2], holes [3], attached pillars [4,5,6] or point-like spring-mass resonators [7,8,9] attached to them has been investigated by several groups, as well as the resonant properties of complex inclusions [10].…”

Section: Introductionmentioning

confidence: 99%

Omnidirectional refractive devices for flexural waves based on graded phononic crystals

Torrent

Pennec

Djafari‐Rouhani

2014

Journal of Applied Physics

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Abstract. Different omnidirectional refractive devices for flexural waves in thin plates are proposed and numerically analyzed. Their realization is explained by means phononic crystal plates, where a previously developed homogenization theory is employed for the design of graded index refractive devices. These devices consist of a circular cluster of inclusions with properly designed gradient in their radius. With this approach, the Luneburg and Maxwell lenses and a family of beam splitters for flexural waves are proposed and analyzed. Results show that these devices work properly in a broadband frequency region, being therefore an efficient approach for the design of refractive devices specially interesting for nano-scale applications.

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Elastic analog of graphene: Dirac cones and edge states for flexural waves in thin plates

Cited by 170 publications

References 38 publications

Waveguiding by a locally resonant metasurface

Waveguiding by a locally resonant metasurface

Effective medium theory for elastic metamaterials in thin elastic plates

Omnidirectional refractive devices for flexural waves based on graded phononic crystals

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