Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Nemat‐Nasser, Sia

doi:10.1016/j.mechmat.2018.12.011

Cited by 27 publications

(5 citation statements)

References 11 publications

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“…To put this result into context, we recall that the first report of negative refraction was for electromagnetic waves, and required a two-dimensional composite made of complicated split ring resonators (Smith et al, 2000, Shelby et al, 2001, Pendry, 2004. Interest in this phenomenon has been disseminated to elastodynamics, accompanied with ongoing studies (Craster and Guenneau, 2012, Bordiga et al, 2019, Nemat-Nasser, 2019. Notably, Willis (2013) was the first to show that a simple laminate is capable of negatively refracting anti-plane shear waves.…”

Section: Introductionmentioning

confidence: 98%

Anomalous energy transport in laminates with exceptional points

Lustig

Elbaz

Muhafra

et al. 2019

Journal of the Mechanics and Physics of Solids

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Recent interest in metamaterials has led to a renewed study of wave mechanics in different branches of physics. Elastodynamics involves a special intricacy, owing to a coupling between the volumetric and shear parts of the elastic waves. Through a study of in-plane waves traversing periodic laminates, we here show that this coupling can result with unusual energy transport. We find that the corresponding frequency spectrum contains modes which simultaneously attenuate and propagate, and demonstrate that these modes coalesce to purely propagating modes at exceptional points-a property that was recently reported in parity-time symmetric systems. We show that the laminate exhibits metamaterial features near these points, such as negative refraction, and beam steering and splitting. While negative refraction in laminates has been demonstrated before by considering pure shear waves impinging an interface with multiple layers, here we realize it for coupled waves impinging a simple single-layer interface. This feature, together with the appearance of exceptional points, are absent from the model problem of anti-plane shear waves which have no volumetric part, and hence from the mathematically identical electromagnetic waves. Our work further paves the way for applications such as asymmetric mode switches, by encircling exceptional points in a tangible, purely elastic apparatus.

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Section: Introductionmentioning

confidence: 98%

Anomalous energy transport in laminates with exceptional points

Lustig

Elbaz

Muhafra

et al. 2019

Journal of the Mechanics and Physics of Solids

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“…Despite the huge difference in the length scale that the two theories were developed for, fascinating realizations of quantum phenomena were demonstrated using macroscopic systems in recent years [2]. Examples include the Hall effect [3,4], geometric phase [5], and negative refraction [6][7][8][9][10]. Special attention is given to extraordinary transport properties based on PT symmetry [11][12][13][14][15][16][17][18], which corresponds to the commutativity of an operator with combined parity-time reversal operators.…”

Section: Introductionmentioning

confidence: 99%

Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

Gal¹,

Moiseyev²

2020

Phys. Rev. Applied

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Recent years have seen a fascinating pollination of ideas from quantum theories to elastodynamics-a theory that phenomenologically describes the time-dependent macroscopic response of materials.Here, we open route to transfer additional tools from non-Hermitian quantum mechanics. We begin by identifying the differences and similarities between the one-dimensional elastodynamics equation and the time-independent Schrödinger equation, and finding the condition under which the two are equivalent. Subsequently, we demonstrate the application of the non-Hermitian perturbation theory to determine the response of elastic systems; calculation of leaky modes and energy decay rate in heterogenous solids with open boundaries using a quantum mechanics approach; and construction of degeneracies in the spectrum of these assemblies. The latter result is of technological importance, as it introduces an approach to harness extraordinary wave phenomena associated with non-Hermitian degeneracies for practical devices, by designing them in simple elastic systems. As an example of such application, we demonstrate how an assembly of elastic slabs that is designed with two degenerate shear states according to our scheme, can be used for mass sensing with enhanced sensitivity by exploiting the unique topology near the exceptional point of degeneracy. arXiv:1910.07306v2 [cond-mat.soft]

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“…Another essential feature of architected periodic structures is their ability to attenuate waves with specific frequencies, i.e., architected periodic structures can stop the propagation of waves with specific frequencies while letting the waves with all other frequencies pass. This exciting feature was first reported by Brillouin [36] and after that, many researchers [37][38][39][40] tried to study bandgap properties of periodic structures to investigate parameters affecting wave propagation in lattice materials and tuning the bandgaps [23,[41][42][43][44][45][46]. This field of research has recently been extended to the design of elastic structures with the ability to actively tune the attenuation zones [47].…”

Section: Introductionmentioning

confidence: 93%

Orientation-dependent mechanical properties of planar microtubule-based bio-nanometamaterials

Jafari¹,

Sepehri²,

Yazdi³

et al. 2020

Phys. Scr.

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Microtubules are protein-based filaments that carry out essential biological roles of eukaryotic cells. They play, in vivo, critical roles in a wide variety of physical situations such as maintaining cell shape, supporting cellular motions, and playing significant roles in both intracellular transport and cellular division. To perform some of these functions, microtubules may need to form different topologies in various orientations. Therefore, the need to introduce different structures of microtubules arises. Orientation-dependent architected structures are a type of periodic architected materials that can exhibit various mechanical properties in different orientations. In the present study, several periodic architectures of various topologies are investigated numerically, and their mechanical properties (elastic modulus, Poisson’s ratio, and natural frequencies) are analyzed in different spatial orientations. For this purpose, the representative volume elements are constructed by considering unit cells of different models aligned in different spatial angles, and their elastic moduli and Poisson’s ratios are obtained by the finite element method. Then the finite element equation of motion for the given structures are solved to find their six natural frequencies. Besides, Bloch’s theorem is implemented to study wave propagation and compare the bandgap widths of the structures in different orientations. It is found that while the elastic properties of some architected structures may increase as the orientation angle increases from zero, for some others, a reduction in the elastic moduli can be observed as the angle rises. Further, it is seen that some structures may exhibit positive (and high) values of Poisson’s ratio in some angles, while for a different orientation, these values turn out to be negative. Also, the effects of orientation angle on the natural frequencies and stop-band performance are observed to be significant in some topologies and negligible in some others. A better understanding of the behavior of architected structures in different orientations may provide new ways to design and manufacture various structures with enhanced and tunable mechanical properties.

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Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Cited by 27 publications

References 11 publications

Anomalous energy transport in laminates with exceptional points

Anomalous energy transport in laminates with exceptional points

Linking Scalar Elastodynamics and Non-Hermitian Quantum Mechanics

Orientation-dependent mechanical properties of planar microtubule-based bio-nanometamaterials

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