Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures

Theocharis, G.; Richoux, Olivier; García, Vicente Romero; Merkel, Aurélien; Tournat, Vincent

doi:10.1088/1367-2630/16/9/093017

Cited by 99 publications

(85 citation statements)

References 45 publications

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“…2(b)). In the lossy case, the losses limit the minimum value of group velocity [19], but in our system slow sound velocity can be achieved in the dispersive band below f HR . The average sound speed in the low frequency range is much lower (50 m/s) than the speed of sound in air.…”

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confidence: 74%

Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption

Jiménez

Huang

Romero‐García

et al. 2016

Applied Physics Letters

302

172

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Using the concepts of slow sound and of critical coupling, an ultra-thin acoustic metamaterial panel for perfect and omnidirectional absorption is theoretically and experimentally conceived in this work. The system is made of a rigid panel with a periodic distribution of thin closed slits, the upper wall of which is loaded by Helmholtz Resonators (HRs). The presence of resonators produces a slow sound propagation shifting the resonance frequency of the slit to the deep sub-wavelength regime (λ/88). By controlling the geometry of the slit and the HRs, the intrinsic visco-thermal losses can be tuned in order to exactly compensate the energy leakage of the system and fulfill the critical coupling condition to create the perfect absorption of sound in a large range of incidence angles due to the deep subwavelength behavior. * noe.jimenez@univ-lemans.fr 1 arXiv:1606.07776v1 [physics.class-ph] Jun 2016The ability to perfectly absorb an incoming wave field in a sub-wavelength material is advantageous for several applications in wave physics as energy conversion [1], time reversal technology [2], coherent perfect absorbers [3] or soundproofing [4] among others. The solution of this challenge requires to solve a complex problem: reducing the geometric dimensions of the structure while increasing the density of states at low frequencies and finding the good conditions to match the impedance to the background medium.A successful approach for increasing the density of states at low frequencies with reduced dimensions is the use of metamaterials. Recently, several possibilities based on these systems have been proposed to design sound absorbing structures which can present simultaneously sub-wavelength dimensions and strong acoustic absorption. One strategy to design these sub-wavelength systems consists of using space-coiling structures [5,6]. Another way is to use sub-wavelength resonators as membranes [4,7] or Helmholtz resonators (HRs) [8,9].Recently, a new type of sub-wavelength metamaterials based on the concept of slow sound propagation have been used to the same purpose. This last type of metamaterials [10][11][12] makes use of its strong dispersion for generating slow-sound conditions inside the material and, therefore, drastically decreasing frequency of the absorption peaks. Hence, the structure thickness becomes deeply sub-wavelength. All of these structures, however, while they bring potentially solutions to reduce the geometric dimensions, face the challenge of impedance mismatch to the background medium.The interaction of an incoming wave with a lossy resonant structure, in particular the impedance matching with the background field, is one of the most studied process in the field of wave physics [1][2][3]. These open systems, at the resonant frequency, are characterized by both the leakage rate of energy (i.e., the coupling of the resonant elements with the propagating medium), and the intrinsic losses of the resonator. The balance between the leakage and the losses activates the condition of critic...

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mentioning

confidence: 74%

Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption

Jiménez

Huang

Romero‐García

et al. 2016

Applied Physics Letters

302

172

View full text Add to dashboard Cite

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“…However, in acoustic metamaterials -and up to now-only few works have systematically consider the interplay between all the above phenomena [10][11][12][13][14] . Particularly, in some works, the combined effects of dissipation and dispersion were studied without considering the nonlinearity 2,[15][16][17][18] ; in this case, the relevance of dissipation was further exploited to the design of perfect absorbers 6,7 . In fact, the majority of works on acoustic metamaterials focus on the linear regime and do not consider the nonlinear response of the structure.…”

Section: Introductionmentioning

confidence: 99%

Bright and gap solitons in membrane-type acoustic metamaterials

et al. 2017

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We study analytically and numerically envelope solitons (bright and gap solitons) in a onedimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement.

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“…Using the effective parameters for the neck and cavity elements given by Equations (7) and (8), the impedance of a Helmholtz resonator including the thermoviscous losses and the "end" correction due to the radiation can be obtained [26].…”

Section: Visco-thermal Losses Modelmentioning

confidence: 99%

Iridescent Perfect Absorption in Critically-Coupled Acoustic Metamaterials Using the Transfer Matrix Method

et al. 2017

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Abstract:The absorption performance of a locally-reacting acoustic metamaterial under oblique incidence is studied. The metamaterial is composed of a slotted panel, each slit being loaded by an array of Helmholtz resonators. The system is analytically studied using the transfer matrix method, accounting for the viscothermal losses both in the resonator elements and in the slits, allowing the representation of the reflection coefficient in the complex frequency plane. We show that by tuning the geometry of the metamaterial, perfect absorption peaks can be obtained on demand at selected frequencies and different angles of incidence. When tilting the incidence angle, the peaks of perfect absorption are shifted in frequency, producing an acoustic iridescence effect similar to the optic iridescence achieved by incomplete band gap. Effectively, we show that in this kind of locally-reacting metamaterial, perfect and omnidirectional absorption for a given frequency is impossible to achieve because the metamaterial impedance does not depend on the incidence angle (i.e., the impedance is a locally reacting one). The system is interpreted in the complex frequency plane by analysing the trajectories of the zeros of the reflection coefficient. We show that the trajectories of the zeros do not overlap under oblique incidence, preventing the observation of perfect and omnidirectional absorption in locally reacting metamaterials. Moreover, we show that for any locally resonant material, the absorption in diffuse field takes a maximal value of 0.951, which is achieved by a material showing perfect absorption for an incidence angle of 50.34 degrees.

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Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures

Cited by 99 publications

References 45 publications

Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption

Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption

Bright and gap solitons in membrane-type acoustic metamaterials

Iridescent Perfect Absorption in Critically-Coupled Acoustic Metamaterials Using the Transfer Matrix Method

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