Designing perturbative metamaterials from discrete models

Matlack, Kathryn H.; Serra-García, Marc; Palermo, Antonio; Huber, Sebastian; Daraio, Chiara

doi:10.1038/s41563-017-0003-3

Cited by 179 publications

(97 citation statements)

References 57 publications

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“…So far, experimental implementations exist on the centimeter scale, both for the case of time-reversal symmetry broken by external driving [1], such as in coupled gyroscopes, as well as for the case without driving [2][3][4][5][6], such as in coupled pendula. Moreover, a multitude of different implementations have been envisioned theoretically [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. However, it is highly desirable to come up with alternative design ideas that may be realized on the nanoscale, eventually pushing towards applications in integrated phononics.…”

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confidence: 99%

Snowflake phononic topological insulator at the nanoscale

et al. 2018

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confidence: 99%

Snowflake phononic topological insulator at the nanoscale

et al. 2018

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“…The acoustic metamaterial context in which we implement gauge fields provides us with significant control [9][10][11] over frequency, wavelength, and attenuation scales unavailable in the analogous electronic realizations. For example, a metamaterial composed of stiff (e.g., metallic) components of micron-scale length may be suitable for control over ultrasound with gigahertz-scale frequencies, whereas cm-scale metamaterials may provide control over kHz-scale sound waves.…”

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confidence: 99%

Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials

et al. 2017

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Mechanical strain can lead to a synthetic gauge field that controls the dynamics of electrons in graphene sheets as well as light in photonic crystals. Here, we show how to engineer an analogous synthetic gauge field for lattice vibrations. Our approach relies on one of two strategies: shearing a honeycomb lattice of masses and springs or patterning its local material stiffness. As a result, vibrational spectra with discrete Landau levels are generated. Upon tuning the strength of the gauge field, we can control the density of states and transverse spatial confinement of sound in the metamaterial. We also show how this gauge field can be used to design waveguides in which sound propagates with robustness against disorder as a consequence of the change in topological polarization that occurs along a domain wall. By introducing dissipation, we can selectively enhance the domain-wall-bound topological sound mode, a feature that may potentially be exploited for the design of sound amplification by stimulated emission of radiation (SASER, the mechanical analogs of lasers). DOI: 10.1103/PhysRevLett.119.195502 Electronic systems subject to a uniform magnetic field experience a wealth of fascinating phenomena such as topological states [1] in the integer quantum Hall effect [2] and anyons associated with the fractional quantum Hall effect [3]. Recently, it has been shown that in a strained graphene sheet, electrons experience external potentials that can mimic the effects of a magnetic field, which results in the formation of Landau levels and edge states [4,5]. Working in direct analogy with this electronic setting, pseudomagnetic fields have been engineered by arranging CO molecules on a gold surface [6] and in photonic honeycomb-lattice metamaterials [7,8].In this Letter, we apply insights about wave propagation in the presence of a gauge field to acoustic phenomena in a nonuniform phononic crystal, using the appropriate mechanisms of strain-phonon coupling and frictional dissipation, in contrast to those present in electronic and photonic cases. The acoustic metamaterial context in which we implement gauge fields provides us with significant control [9-11] over frequency, wavelength, and attenuation scales unavailable in the analogous electronic realizations. For example, a metamaterial composed of stiff (e.g., metallic) components of micron-scale length may be suitable for control over ultrasound with gigahertz-scale frequencies, whereas cm-scale metamaterials may provide control over kHz-scale sound waves. We develop two strategies for realizing a uniform pseudomagnetic field in a metamaterial based on the honeycomb lattice, i.e., "mechanical graphene" [12]. In the first strategy, we apply stress at the boundary to obtain nonuniform strain in the bulk, which leads to a Landau-level spectrum, whereas in the second strategy, we exploit builtin, nonuniform patterning of the local metamaterial stiffness. This second strategy shows how the unique controllability of metamaterials can lead to novel designs inaccessibl...

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“…2 covers frequencies ranging between 20 and 200 Hz. The index i used in the figures denotes the index of the coefficient in the series (1). The triangular markers always lie below the circular ones, so that results clearly indicate that the computed Fourier coefficients for the cloaked void have moduli remarkably smaller than those pertaining to the uncloaked void.…”

Section: Evaluation Of the Multipole Coefficients For The Scattered Fmentioning

confidence: 96%

“…Published in Proceedings of the Royal Society A (2019), 475, 20190283 doi: 10.1098/rspa.2019.0283 Fig. 2: Fourier coefficients for the representation of the scattered displacement around a square void in a structured plate subject to sinusoidal vibration, note that index i is pertinent to the series (1). Frequencies range between 20 and 200 Hz and coefficients are evaluated with reference to the two circular contours of the radii R 1 =130 mm and R 2 =150 mm.…”

Section: Elastic Platesmentioning

confidence: 99%

Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates

2019

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In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analyzed, but still unchallenged, mechanical problem. The 'cloaking transformation' concept, originally developed in electromagnetism and optics, is not directly applicable to elastic waves, displaying a complex vectorial nature. Consequently, all examples of elastic cloaking presented so far involve complex design and thick coating skins. These cloakings often work only for problems of unidirectional propagation, within narrow ranges of frequency, and considering only one colaked object. Here, a new method based on the concept of reinforcement, achieved via elastic stiffening and mass redistribution, is introduced to cloak multiple voids in an elastic plate. This simple technique produces invisibility of the voids to flexural waves within an extremely broad range of frequencies and thus surpassing in many aspects all existing cloaking techniques. The proposed design principle is applicable in mechanical problems ranging from the micro-scale to the scale of civil engineering. For instance, our results show how to design a perforated load-bearing building wall, vibrating during an earthquake exactly as the same wall, but unperforated, a new finding for seismic protection.

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Designing perturbative metamaterials from discrete models

Cited by 179 publications

References 57 publications

Snowflake phononic topological insulator at the nanoscale

Snowflake phononic topological insulator at the nanoscale

Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials

Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates

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