Homogenized enriched continuum analysis of acoustic metamaterials with negative stiffness and double negative effects

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This paper demonstrates the application of a recently developed enriched micro-inertial continuum based homogenization framework towards numerical dispersion and boundary value problem analyses of local resonance metamaterials exhibiting sub-wavelength negative stiffness and double negative effects (i.e. simultaneous negative effective mass density and stiffness). This is a novel development since homogenized structural dynamic analyses that specifically incorporate negative stiffness effects have not yet been extensively explored. The proposed methodology is successful in approximating the negative stiffness effect to a certain degree. Accordingly, an appropriate error estimation procedure based on dispersion analyses is proposed to identify the limits of the reliability of the homogenized model. The resulting methodology provides a highly efficient framework for the analysis of double negative metamaterial problems involving a non-trivial macroscopic loading, the influence of the applied boundary conditions, and a complex unit cell design. This is illustrated through a case study involving the refraction analysis of a double negative metamaterial prism.

Originele taal-2Engels
Pagina's (van-tot)104-117
Aantal pagina's14
TijdschriftJournal of the Mechanics and Physics of Solids
Volume119
DOI's
StatusGepubliceerd - 1 okt 2018

Vingerafdruk

Metamaterials
stiffness
Acoustics
Stiffness
continuums
acoustics
methodology
dynamic structural analysis
Structural dynamics
homogenizing
Prisms
Refraction
boundary value problems
Error analysis
Boundary value problems
prisms
refraction
Boundary conditions
boundary conditions
Wavelength

Citeer dit

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title = "Homogenized enriched continuum analysis of acoustic metamaterials with negative stiffness and double negative effects",
abstract = "This paper demonstrates the application of a recently developed enriched micro-inertial continuum based homogenization framework towards numerical dispersion and boundary value problem analyses of local resonance metamaterials exhibiting sub-wavelength negative stiffness and double negative effects (i.e. simultaneous negative effective mass density and stiffness). This is a novel development since homogenized structural dynamic analyses that specifically incorporate negative stiffness effects have not yet been extensively explored. The proposed methodology is successful in approximating the negative stiffness effect to a certain degree. Accordingly, an appropriate error estimation procedure based on dispersion analyses is proposed to identify the limits of the reliability of the homogenized model. The resulting methodology provides a highly efficient framework for the analysis of double negative metamaterial problems involving a non-trivial macroscopic loading, the influence of the applied boundary conditions, and a complex unit cell design. This is illustrated through a case study involving the refraction analysis of a double negative metamaterial prism.",
keywords = "Acoustic metamaterial, Dispersion spectrum, Double negativity, Homogenization, Local resonance, Multiscale analysis",
author = "A. Sridhar and L. Liu and V.G. Kouznetsova and M.G.D. Geers",
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month = "10",
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language = "English",
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journal = "Journal of the Mechanics and Physics of Solids",
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}

Homogenized enriched continuum analysis of acoustic metamaterials with negative stiffness and double negative effects. / Sridhar, A.; Liu, L.; Kouznetsova, V.G.; Geers, M.G.D.

In: Journal of the Mechanics and Physics of Solids, Vol. 119, 01.10.2018, blz. 104-117.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

T1 - Homogenized enriched continuum analysis of acoustic metamaterials with negative stiffness and double negative effects

AU - Sridhar, A.

AU - Liu, L.

AU - Kouznetsova, V.G.

AU - Geers, M.G.D.

PY - 2018/10/1

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N2 - This paper demonstrates the application of a recently developed enriched micro-inertial continuum based homogenization framework towards numerical dispersion and boundary value problem analyses of local resonance metamaterials exhibiting sub-wavelength negative stiffness and double negative effects (i.e. simultaneous negative effective mass density and stiffness). This is a novel development since homogenized structural dynamic analyses that specifically incorporate negative stiffness effects have not yet been extensively explored. The proposed methodology is successful in approximating the negative stiffness effect to a certain degree. Accordingly, an appropriate error estimation procedure based on dispersion analyses is proposed to identify the limits of the reliability of the homogenized model. The resulting methodology provides a highly efficient framework for the analysis of double negative metamaterial problems involving a non-trivial macroscopic loading, the influence of the applied boundary conditions, and a complex unit cell design. This is illustrated through a case study involving the refraction analysis of a double negative metamaterial prism.

AB - This paper demonstrates the application of a recently developed enriched micro-inertial continuum based homogenization framework towards numerical dispersion and boundary value problem analyses of local resonance metamaterials exhibiting sub-wavelength negative stiffness and double negative effects (i.e. simultaneous negative effective mass density and stiffness). This is a novel development since homogenized structural dynamic analyses that specifically incorporate negative stiffness effects have not yet been extensively explored. The proposed methodology is successful in approximating the negative stiffness effect to a certain degree. Accordingly, an appropriate error estimation procedure based on dispersion analyses is proposed to identify the limits of the reliability of the homogenized model. The resulting methodology provides a highly efficient framework for the analysis of double negative metamaterial problems involving a non-trivial macroscopic loading, the influence of the applied boundary conditions, and a complex unit cell design. This is illustrated through a case study involving the refraction analysis of a double negative metamaterial prism.

KW - Acoustic metamaterial

KW - Dispersion spectrum

KW - Double negativity

KW - Homogenization

KW - Local resonance

KW - Multiscale analysis

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