Generalized analytic model for rotational and anisotropic metasolids

An analytical approach is presented to model a metasolid accounting for anisotropic effects and rotational mode. The metasolid is made of either cylindrical or spherical hard inclusions embedded in a stiff matrix via soft claddings . It is shown that such a metasolid exhibits negative mass densities...

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Published inJournal of physics communications Vol. 2; no. 3; p. 35035
Main Authors Favier, Elie, Nemati, Navid, Perrot, Camille, He, Qi-Chang
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 21.03.2018
Subjects
acoustic metamaterials
Acoustics
effective density of moment of inertia
effective-medium parameters
elastic metamaterials
homogenization
Inertia
local resonances
Mechanics
Physics
rotational motions
low frequencies
homogenization
axial translation
effective-medium parameters
rotation
local resonances
elastic metamaterials
acoustic metamaterials
rotational motions
local resonance
effective density of moment of inertia
band gap
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Abstract An analytical approach is presented to model a metasolid accounting for anisotropic effects and rotational mode. The metasolid is made of either cylindrical or spherical hard inclusions embedded in a stiff matrix via soft claddings . It is shown that such a metasolid exhibits negative mass densities near the translational-mode resonances, and negative density of moment of inertia near the rotational resonances. As such, the effective density of moment of inertia is introduced to characterize the homogenized material with respect to its rotational mode. The results obtained by this analytical continuum approach are compared with those from discrete mass-spring model, and the validity of the latter is discussed. Based on derived analytical expressions, we study how different resonance frequencies associated with different modes vary and are placed with respect to each other, in function of the mechanical properties of the coating layer. We demonstrate that the resonances associated with additional modes that are taken into account, i.e., axial translation for cylinders, and rotations for both cylindrical and spherical systems, can occur at lower frequencies compared with the previously studied plane-translational modes.
AbstractList An analytical approach is presented to model a metasolid accounting for anisotropic effects and rotational mode. The metasolid is made of either cylindrical or spherical hard inclusions embedded in a stiff matrix via soft claddings . It is shown that such a metasolid exhibits negative mass densities near the translational-mode resonances, and negative density of moment of inertia near the rotational resonances. As such, the effective density of moment of inertia is introduced to characterize the homogenized material with respect to its rotational mode. The results obtained by this analytical continuum approach are compared with those from discrete mass-spring model, and the validity of the latter is discussed. Based on derived analytical expressions, we study how different resonance frequencies associated with different modes vary and are placed with respect to each other, in function of the mechanical properties of the coating layer. We demonstrate that the resonances associated with additional modes that are taken into account, i.e., axial translation for cylinders, and rotations for both cylindrical and spherical systems, can occur at lower frequencies compared with the previously studied plane-translational modes.
Author Nemati, Navid
Perrot, Camille
Favier, Elie
He, Qi-Chang
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  organization: Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France
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crossref_primary_10_1093_jom_ufae044
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Issue 3
Keywords low frequencies
homogenization
axial translation
effective-medium parameters
rotation
local resonances
elastic metamaterials
acoustic metamaterials
rotational motions
local resonance
effective density of moment of inertia
band gap
Language English
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Snippet An analytical approach is presented to model a metasolid accounting for anisotropic effects and rotational mode. The metasolid is made of either cylindrical or...
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StartPage 35035
SubjectTerms acoustic metamaterials
Acoustics
effective density of moment of inertia
effective-medium parameters
elastic metamaterials
homogenization
Inertia
local resonances
Mechanics
Physics
rotational motions
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Title Generalized analytic model for rotational and anisotropic metasolids
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