Unified homogenization of photonic/phononic crystals with first-band negative refraction

Nemat‐Nasser, Sia

doi:10.1016/j.mechmat.2016.10.010

Cited by 15 publications

(4 citation statements)

References 47 publications

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“…At first this may appear surprising since a counterpart does not exist for two-dimensional photonic crystals, nor for phononic crystals in anti-plane shearing, where negative refraction on the acoustic branch can be realized only if we use an anisotropic matrix material [9,5]. The EM properties of an isotropic material are completely defined by an electric permittivity, , and a magnetic permeability, µ.…”

Section: (Left)mentioning

confidence: 99%

“…Hence their acoustic branch contains only one (dilatational) passband involving positive refraction only. It is known that photonic and phononic crystals with anisotropic constituents can display negative refraction on their acoustic branch [9,5], but this has not been demonstrated experimentally. We point out that, using numerical simulations, negative refraction has been shown [10] to be possible on a narrow region of the acoustic branch of a photonic crystal consisting of circular holes placed in a square-lattice pattern within a homogeneous and isotropic dielectric matrix.…”

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confidence: 99%

“…Similarly periodic elastic composites consisting of periodically distributed elastic inclusions in an elastic matrix exhibit band structure [3], negative refraction [4], and effective properties that are frequency-dependent [5]. Early experimental demonstrations of negative refraction and focusing properties of phononic crystals have employed water as the matrix material, within which stiff inclusions are periodically distributed, revealing negative refraction on the second (optical branch) passband [6,7,8].…”

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confidence: 99%

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Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Nemat‐Nasser

2019

Mechanics of Materials

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Guided by theoretical predictions, we have demonstrated experimentally the existence of negative refraction on the two lowest acoustic-branch passbands (shear and longitudinal modes) of a simple two-dimensional phononic crystal consisting of an isotropic stiff (aluminum) matrix and square-patterned isotropic compliant (PMMA) circular inclusions. At frequencies and wave vectors where the refraction on the acoustic-branch passbands is negative, the effective mass-density and the effective stiffness tensors of the crystal are positive-definite, and this is an inherent property of such phononic crystals. The equi-frequency contours and energy flux vectors as fuctions of the phase-vector components, reveal a rich body of refractive properties that can be exploited to realize, for example, beam splitting, focusing, and frequency filtration on the lowest passbands of the crystal where the dissipation is minimum. By proper selection of material and geometric parameters these phenomena can be realized at remarkably low frequencies (large wave lengths) using rather small simple two-phase unit cells.

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confidence: 99%

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Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Nemat‐Nasser

2019

Mechanics of Materials

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“…Phononic crystals as periodic structures can give rise to complete band gaps in which the elastic wave cannot propagate. Thus, they have the ability to control the propagation and vibration of elastic waves, and considerable attention has been focused in the past few decades [1][2][3][4][5]. In recent years, the rapid development of phononic crystals leads to the emergency of a new kind of artificial structures as the elastic metamaterials [6][7][8][9][10][11][12].…”

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confidence: 99%

Tunable mechanical diode of nonlinear elastic metamaterials induced by imperfect interface

Wang

2021

Proc. R. Soc. A.

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In this investigation, the non-reciprocal transmission in a nonlinear elastic metamaterial with imperfect interfaces is studied. Based on the Bloch theorem and stiffness matrix method, the band gaps and transmission coefficients with imperfect interfaces are obtained for the fundamental and double frequency cases. The interfacial influences on the transmission behaviour are discussed for both the nonlinear phononic crystal and elastic metamaterial. Numerical results for the imperfect interface structure are compared with those for the perfect one. Furthermore, experiments are performed to support the theoretical analysis. The present research is expected to be helpful to design tunable devices with the non-reciprocal transmission and diode behaviour of the elastic metamaterial.

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Elastic wave scattering by a pair of parallel semi-infinite cracks in mechanical metamaterials with multi resonators

et al. 2021

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As emerging artificial structures, elastic wave metamaterials can show some unique properties in special frequency regions. In this study, the elastic wave scattering by a pair of parallel semi-infinite cracks in mechanical metamaterials with local resonators is studied. According to the discrete Wiener-Hopf method, the far field displacement solution is obtained. At the same time, the dynamic negative effective mass and band gaps can be observed with local resonators. Our attention is focused on how the internal microstructure affects the crack faces. Numerical results show that because of the stop band, the crack can be prevented from being disturbed by incident waves in specific frequency regions. As a result, the possibility of crack initiation and instability propagation is reduced considerably. This present work is expected to provide a way to improve arrest performance of elastic waves metamaterials.

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Unified homogenization of photonic/phononic crystals with first-band negative refraction

Cited by 15 publications

References 47 publications

Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Tunable mechanical diode of nonlinear elastic metamaterials induced by imperfect interface

Elastic wave scattering by a pair of parallel semi-infinite cracks in mechanical metamaterials with multi resonators

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