A two-way model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators

Mercier, Jean‐François; Lombard, Bruno

doi:10.1016/j.wavemoti.2017.04.004

Cited by 3 publications

(3 citation statements)

References 41 publications

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“…Extending our time-domain approach to nonlinear acoustic metamaterials would therefore be a fruitful contribution to this research effort. Preliminary works have been done on that subject: the propagation of nonlinear acoustic waves in a tube coupled with Helmholtz resonators has been addressed theoretically in [31,34] and experimentally in [40], by considering one-way propagation. Considering two-way propagation will pave the way to the simulation of wave phenomena in nonlinear acoustic metamaterials.…”

Section: Resultsmentioning

confidence: 99%

Simulating transient wave phenomena in acoustic metamaterials using auxiliary fields

Bellis

Lombard

2019

Wave Motion

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Acoustic wave propagation in dispersive metamaterials is considered. A prototypical example stems from the homogenization of a waveguide coupled with Helmholtz resonators and elastic membranes. The homogenized models of acoustic metamaterials are characterized by constitutive parameters, namely the effective bulk modulus and the effective mass density, that are frequency dependent. In this context, the objective considered here is to analyze such media in the time-domain and to simulate associated transient wave phenomena. To do so, the governing evolution equations are recast using a set of auxiliary fields to obtain an augmented first-order hyperbolic system. This initial-value problem is analyzed and then solved numerically using a splitting method and a high-order finite-difference scheme. An immersed interface method is also implemented to tackle scattering and interface problems involving metamaterial subdomains of arbitrary shapes. Numerical experiments are performed to validate the proposed overall approach and to investigate a variety of transient wave phenomena occurring in acoustic metamaterials.

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Section: Resultsmentioning

confidence: 99%

Simulating transient wave phenomena in acoustic metamaterials using auxiliary fields

Bellis

Lombard

2019

Wave Motion

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“…The Boussinesq-type models have been recently used to study the scattering of long longitudinal bulk strain solitary waves by delamination in [22,23,24], and some related experimental observations have been reported in [25,26]. We also note the related studies on nonlinear wave scattering by defects in lattices [27] and strings [28]. Some other Boussinesq-type models have been derived to describe the propagation of large amplitude transverse waves (see [29] and references therein).…”

Section: Introductionmentioning

confidence: 92%

On Boussinesq-type models for long longitudinal waves in elastic rods

2019

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In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesqtype model, and extend these derivations to include axially symmetric loading on the lateral boundary surface, and longitudinal pre-stretch. We systematically derive two forced Boussinesq-type models from the full equations of motion and non-zero surface boundary conditions, utilising the presence of two small parameters characterising the smallness of the wave amplitude and the long wavelength compared to the radius of the waveguide. We compare the basic dynamical properties of both models (linear dispersion curves and solitary wave solutions). We also briefly describe the laboratory experiments on generation of bulk strain solitary waves in the Ioffe Institute, and suggest that this generation process can be modelled using the derived equations.

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“…Subsequently, the Sugimoto's model has led to numerical, experimental and theoretical works [25,35,31]. Enrichment of this model, in particular by taking into account nonlinear attenuation mechanisms in (1.1b), have led to the first experimental observation of acoustic solitons [35].…”

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confidence: 99%

Analysis of a Sugimoto Model of Nonlinear Acoustics in an Array of Helmholtz Resonators

Junca¹,

Lombard²

2020

SIAM J. Appl. Math.

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A coupled system involving a nonlinear scalar PDE and a linear ODE is theoretically investigated. This hypebolic system with relaxation models the propagation of nonlinear waves in a waveguide connected to Helmholtz resonators, this device being an example of a nonlinear acoustic metamaterial. In a previous paper [Sugimoto, J. Fluid. Mech. 1992], it has been shown that this device allows also the propagation of acoustic solitons. In the present paper, the mathematical properties of the coupled system are analysed: formation of singularity in finite time, existence of entropy solutions in fractional BV spaces and uniqueness with a single family of entropies. New results are also deduced about weakly coupled systems. Numerical simulations illustrate these findings.

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A two-way model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators

Cited by 3 publications

References 41 publications

Simulating transient wave phenomena in acoustic metamaterials using auxiliary fields

Simulating transient wave phenomena in acoustic metamaterials using auxiliary fields

On Boussinesq-type models for long longitudinal waves in elastic rods

Analysis of a Sugimoto Model of Nonlinear Acoustics in an Array of Helmholtz Resonators

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