Elastic wave near-cloaking

Quadrelli, Davide Enrico; Kadic, Muamer; Braghin, Francesco

doi:10.1016/j.eml.2021.101262

Cited by 21 publications

(13 citation statements)

References 37 publications

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“…Topical examples include analogies to the Quantum Hall effect (QH) [11][12][13], Quantum Spin Hall effect (QSH) [14][15][16], and Quantum Valley Hall effect (QVH) [17][18][19], which have been employed for the fabrication of scattering-immune waveguides with unprecedented energy transfer capabilities. Also, wave focusing [20], mode conversion [21,22], as well as cloaking [23][24][25][26] have recently been observed in mechanics and acoustics. An emerging trend leverages temporal (active) modulations of elastic or physical parameters [27] to accomplish different tasks, such as nonreciprocity [28][29][30][31][32][33][34][35], parametric amplification [36], frequency conversion [37] and edge-toedge pumping [38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 95%

Adiabatic edge-to-edge transformations in time-modulated elastic lattices and non-Hermitian shortcuts

Riva,

Castaldini,

Braghin

2021

Preprint

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The temporal modulation of a relevant parameter can be employed to induce modal transformations in Hermitian elastic lattices. When this is combined with a proper excitation mechanism, it allows to drive the energy transfer across the lattice with tunable propagation rates. Such a modal transformation, however, is limited by the adiabaticity of the process, which dictates an upper bound for the modulation speed. In this manuscript, we employ a non-Hermitian shortcut by way of a tailored gain and loss to violate the adiabatic limit and, therefore, to achieve superfast modal transformations. A quantitative condition for adiabaticity is firstly derived and numerically verified for a pair of weakly coupled time-dependent mechanical oscillators, which can be interpreted in the light of modal interaction between crossing states. It is shown that for sufficiently slow time-modulation, the elastic energy can be transferred from one oscillator to the other. A non-Hermitian shortcut is later induced to break the modal coupling and, therefore, to speed-up the modal transformation. The strategy is then generalized to elastic lattices supporting topological edge states. We show that the requirements for a complete edge-to-edge energy transfer are lifted from the adiabatic limit toward higher modulation velocities, opening up new opportunities in the context of wave manipulation and control.

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Section: Introductionmentioning

confidence: 95%

Adiabatic edge-to-edge transformations in time-modulated elastic lattices and non-Hermitian shortcuts

Riva,

Castaldini,

Braghin

2021

Preprint

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“…Some of the most commonly studied of such properties are negative Poisson's ratio [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29] (auxetic behaviour), negative stiffness [30,31,32,33,34] and negative compressibility [35,36]. Over the last thirty years, it has been demonstrated that devices utilising materials exhibiting such characteristics can be used in the case of a variety of applications including protective devices [37,38], sports equipment [39] as well as biomedical [40,41] and vibration damping devices [42,43,44]. One of the most studied of these unusual mechanical properties seems to be auxetic behaviour where the keen interest of researchers in this property stems from the fact that auxetic materials often exhibit high indentation resistance [45], wave attenuation [46,47] and many other features that are useful in the case of various applications.…”

Section: Introductionmentioning

confidence: 99%

“…[35,36] Over the past 30 years, it has been demonstrated that devices utilizing materials exhibiting such characteristics can be used in the case of a variety of applications including protective devices, [37,38] sports equipment, [39] as well as biomedical [40,41] and vibration damping devices. [42][43][44] One of the most studied of these unusual mechanical properties seems to be auxetic behavior where the keen interest of researchers in this property stems from the fact that auxetic materials often exhibit high indentation resistance, [45] wave attenuation, [46,47] and many other features that are useful in the case of various applications. The commercial appeal of auxetic mechanical metamaterials resulted in a broad range of studies focused on different types of mechanical structures.…”

Section: Introductionmentioning

confidence: 99%

Variable Dual Auxeticity of the Hierarchical Mechanical Metamaterial Composed of Re‐Entrant Structural Motifs

Dudek

Martínez

Kadic

2022

Physica Status Solidi (b)

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In this work, a novel hierarchical mechanical metamaterial is proposed that is composed of re-entrant truss-lattice elements. It is shown that this system can deform very differently and can exhibit a versatile extent of the auxetic behaviour depending on a small change in the thickness of its hinges. In addition, depending on which hierarchical level is deforming, the whole structure can exhibit a different type of auxetic behaviour that corresponds to a unique deformation mechanism. This results in a dual auxetic structure where the interplay between the two auxetic mechanisms determines the evolution of the system. It is also shown that depending on the specific deformation pattern, it is possible to observe a very different behaviour of the structure in terms of frequencies of waves that can be transmitted through the system. In fact, it is demonstrated that even a very small change in the parametric design of the system may result in a significantly different band gap formation that can be useful in the design of tunable vibration dampers or sensors. The possibility of controlling the extent of the auxeticity also makes the proposed metamaterial to be very appealing from the point of view of protective and biomedical devices.

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“…Modulated materials are key for many desired dynamic properties in the context of phononic structures and can be regarded as building blocks for the implementation of complex systems with unusual functionalities. Among the relevant works, topological waveguides [1][2][3][4][5][6][7], cloaking [8][9][10][11], rainbow devices [12][13][14][15], lenses [16], should be mentioned. These examples offer non-conventional energy transfer mechanisms and rely on passive geometries, stiffness modulations, and symmetry breaks, which have been sought in analogy to similar behaviors previously observed in different realms of physics.…”

Section: Introductionmentioning

confidence: 99%

Harnessing $\mathcal{PT}$-symmetry in non-Hermitian stiffness-modulated waveguides

Riva

2022

Preprint

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The recent progress in the context of elastic metamaterials and modulated waveguides with digitally controllable properties has opened new pathways to overcome the limitations dictated by Hermitian Hamiltonians in mechanics. Among the possible implementations, non-Hermitian, PTsymmetric systems with balanced gain and loss have emerged as an elegant mechanism to access novel functionalities by lifting the non-Hermitian degeneracies (exceptional points). Motivated by this, the paper deals with a non-Hermitian and PT -symmetric elastic waveguide with complex stiffness-modulation. The strength of the stiffness-modulations, tailored in the form of a balanced gain/loss, delineates a transition from unbroken to broken PT -symmetric phases, where distinct Bloch-wave modes coalesce into exceptional points. It is shown that, in the unbroken PT -symmetric regime, and due to the interplay between real and imaginary components of the elasticity, the waveguide operates as a phononic filter. When the strength of the gain/loss interactions increases, the frequency gap closes and the bulk bands degenerate into an exceptional point, where the system operates as a waveguide with asymmetric scattering capabilities. The paper provides a connection between the distinct wave modes that populate the non-Hermitian degeneracies and the directional reflection/transmission capabilities. The asymmetric behavior is herein explained by combining the dispersion properties of a PT -symmetric rod, obtained through the plane wave expansion method (PWEM), and the scattering matrix method (SMM) for a modulated slab series-connected to semi infinite media.

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Elastic wave near-cloaking

Cited by 21 publications

References 37 publications

Adiabatic edge-to-edge transformations in time-modulated elastic lattices and non-Hermitian shortcuts

Adiabatic edge-to-edge transformations in time-modulated elastic lattices and non-Hermitian shortcuts

Variable Dual Auxeticity of the Hierarchical Mechanical Metamaterial Composed of Re‐Entrant Structural Motifs

Harnessing $\mathcal{PT}$-symmetry in non-Hermitian stiffness-modulated waveguides

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