Design of acoustic metamaterials made of Helmholtz resonators for perfect absorption by using the complex frequency plane

Romero‐García, Vicente; Jiménez, Noé; Theocharis, G.; Achilleos, V.; Merkel, Aurélien; Richoux, Olivier; Tournat, Vincent; Groby, J.-P.; Pagneux, Vincent

doi:10.5802/crphys.32

Cited by 26 publications

(27 citation statements)

References 82 publications

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“…In (34), the evolution equation satisfied by G r involves ∂ t ∆V a . This term could be replaced by ∆ div Σ a via conservation laws.…”

Section: Formalism Of Auxiliary Fieldsmentioning

confidence: 99%

“…The corresponding homogenized model is given by (34). Due to the energy considerations mentionned in Section 3, the thickness of the enlarged interface is chosen such that a = e. The effective parameters used in these jump conditions are given in Tables 1 and 2 (34). approximation of the homogenized solution is obtained using the numerical method presented in Section 4.…”

Section: Microstructured and Homogenized Configurationsmentioning

confidence: 99%

“…Once the numerical method validated, for a mesh size enough small, we compare the numerical simulations in the microstructured configuration and for the homogenized problem to assess the reliability of the jump conditions (34).…”

Section: Validation Of the Homogenized Modelmentioning

confidence: 99%

“…In the previous example, we had a X 2 -invariance in the homogenized problem with consequently no role of the effective parameters B 2 , C 12 and C 22 in (34). In this section, we consider the illumination by a source point (51) located at X S = (−35, 0) m so that all the effective parameters are taken into account.…”

Section: Source Pointmentioning

confidence: 99%

“…The two mechanisms of the energy absorption (resonance of the inclusions yielding band-gaps, and dissipative effects in the materials) are discussed in [16,19]. The Coherent Perfect Absorption of dissipative resonant metasurfaces (especially based on Helmholtz resonators) has motivated series of papers [35,13,14,15,17,33,34]. In all these works, the analysis of the scattering matrix is based on the calculation of the wave field at the microstructure scale, which can be computationnaly cumbersome.…”

Section: Introductionmentioning

confidence: 99%

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Damping in a row of locally-resonant inclusions: Dynamic homogenization and scattering of transient shear waves

2021

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The scattering of scalar waves by a periodic row of inclusions is theoretically and numerically investigated. The wavelength in the background medium is assumed to be much larger than the typical sizes of the inclusions. The latter are also much softer than the matrix, yielding localized resonances within the microstructure. Previous works in the inviscid case have concerned: (i) the derivation of effective resonant jump conditions, that are non local in time (Touboul et al., J. Elasticity, 2020); (ii) the introduction of auxiliary fields along the interface, providing a time-domain formulation of the scattering problem (Touboul et al., J. Comput. Phys., 2020). The present contribution extends the analysis to dissipative cases, which allows to be closer from real devices. The effective jump conditions with damping are obtained, both in the frequency domain and in the time domain. An exact plane-wave solution is proposed. A balance of energy is written, and new auxiliary fields are introduced. Practical implementation of the simulation methods is discussed. Then, numerical experiments are proposed to validate the auxiliary-field approach. The effect of dissipation is examined, and the relevance of the homogenized simulations in comparison with full-field simulations of transient waves is assessed. As an application, a numerical experiment of Coherent Perfect Absorption is finally proposed: at critical values of the attenuation parameter and close to the resonant frequencies, the waves impacting the dissipative resonant interface are fully absorbed.

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“…In (34), the evolution equation satisfied by G r involves ∂ t ∆V a . This term could be replaced by ∆ div Σ a via conservation laws.…”

Section: Formalism Of Auxiliary Fieldsmentioning

confidence: 99%

Section: Microstructured and Homogenized Configurationsmentioning

confidence: 99%

Section: Validation Of the Homogenized Modelmentioning

confidence: 99%

Section: Source Pointmentioning

confidence: 99%