Negative group velocity from resonances in two-dimensional phononic crystals

Ao, Xianyu; Chan, Che Ting

doi:10.1080/17455031003610945

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…The region of the dispersion curve with negative slope means a spectral range where the phase and group velocities are opposite in direction. Some researchers 25,30,[36][37][38] have termed the backward-wave phenomenon along with "negative group velocity" simply because, perhaps, in the x-q diagram the slope of the dispersion curve is negative. For example, let us refer to the dispersion diagram in Fig.…”

Section: Discussionmentioning

confidence: 99%

“…1, [20][21][22] Nevertheless, it has been shown that the negative refraction can be achieved not only by metamaterials with double negative properties, but also by Bragg scattering in periodic lattices 23 and others. 24,25 The similarity between these mechanisms relies on negative slope of dispersion curves in the first quadrant of dispersion relations.…”

Section: Introductionmentioning

confidence: 99%

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Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young’s modulus

Huang

Sun²

2012

The Journal of the Acoustical Society of America

105

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A mechanical model representing an acoustic metamaterial that exhibits simultaneously negative mass density and negative Young's modulus was proposed. Wave propagation was studied in the frequency range of double negativity. In view of positive energy flow, it was found that the phase velocity in this range is negative. This phenomenon was also observed using transient wave propagation finite-element analyses of a transient sinusoidal wave and a transient wave packet. In contrast to wave propagation in the region of positive mass and modulus, the peculiar backward wave motion in the region of double negativity was clearly displayed.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young’s modulus

Huang

Sun²

2012

The Journal of the Acoustical Society of America

105

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show abstract

“…Until now, metadamping has been demonstrated with the aid of a locally resonant material possessing a dipole resonance (DP). However, locally resonant material designs featuring monopolar 41 and quadripolar 42,43 resonances appear in the literature. This motivates a study of what effect the type of resonance has on the material dissipation capacity.…”

Section: B Effect Of Local Resonance Typementioning

confidence: 99%

Viscous-to-viscoelastic transition in phononic crystal and metamaterial band structures

Frazier

Hussein

2015

The Journal of the Acoustical Society of America

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The dispersive behavior of phononic crystals and locally resonant metamaterials is influenced by the type and degree of damping in the unit cell. Dissipation arising from viscoelastic damping is influenced by the past history of motion because the elastic component of the damping mechanism adds a storage capacity. Following a state-space framework, a Bloch eigenvalue problem incorporating general viscoelastic damping based on the Zener model is constructed. In this approach, the conventional Kelvin-Voigt viscous-damping model is recovered as a special case. In a continuous fashion, the influence of the elastic component of the damping mechanism on the band structure of both a phononic crystal and a metamaterial is examined. While viscous damping generally narrows a band gap, the hereditary nature of the viscoelastic conditions reverses this behavior. In the limit of vanishing heredity, the transition between the two regimes is analyzed. The presented theory also allows increases in modal dissipation enhancement (metadamping) to be quantified as the type of damping transitions from viscoelastic to viscous. In conclusion, it is shown that engineering the dissipation allows one to control the dispersion (large versus small band gaps) and, conversely, engineering the dispersion affects the degree of dissipation (high or low metadamping).

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“…The prefix meta-(meaning "beyond") is associated with the notion that through deliberate design of the internal structure, these materials manifest unusual properties that exceed those of conventional composites and phononic crystals. In the context of wave propagation, local resonances are generally the key feature in metamaterials leading to salient properties such as subwavelength band gaps [9][10][11][12], negative effective material properties [13][14][15][16], enhanced dissipation [17][18][19], and thermal conductivity reduction [20], among others.At present, much of the phenomena of wave propagation in phononic materials is understood from the perspective of conservative linear elasticity. Realizing their full potential, however, requires an account of energy dissipation from damping.…”

mentioning

confidence: 99%

Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex

Frazier

Hussein

2016

Comptes Rendus. Physique

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It is common for dispersion curves of damped periodic materials to be based on real frequencies versus complex wavenumbers or, conversely, real wavenumbers versus complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained.

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Negative group velocity from resonances in two-dimensional phononic crystals

Cited by 5 publications

References 25 publications

Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young’s modulus

Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young’s modulus

Viscous-to-viscoelastic transition in phononic crystal and metamaterial band structures

Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex

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