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

Sridhar, A.; Liu, Lei; Kouznetsova, V Varvara; Geers, M.G.D.

doi:10.1016/j.jmps.2018.06.015

Cited by 45 publications

(23 citation statements)

References 38 publications

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“…[109] Sridhar et al introduced a local resonance metamaterial with sub-wavelength negative stiffness and simultaneous negative equivalent mass density and stiffness. [110] As shown in Figure 21, the negative stiffness effects necessary for the double-negative passband are generated by the outer resonators.…”

Section: Negative Stiffnessmentioning

confidence: 99%

“…Although some scholars have conducted 3D structural research considering waves in any given direction, [16,24,31,32,55,61,62,108,129] most of the existing studies are based on the 2D simplified model to analyze the propagation of waves. [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]55,56,58,59,[61][62][63][64][65][66]68,70,[106][107][108]110,[112][113][114][116][117][118]…”

Section: Structure Dimensionmentioning

confidence: 99%

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A Review of Research on Seismic Metamaterials

Shu

Zhao

et al. 2020

Adv Eng Mater

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Section: Negative Stiffnessmentioning

confidence: 99%

Section: Structure Dimensionmentioning

confidence: 99%

A Review of Research on Seismic Metamaterials

Shu

Zhao

et al. 2020

Adv Eng Mater

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“…Alternatively, restricted to linear elasticity, Sridhar et al [16] combined the framework of Pham et al [15] with dynamic model reduction techniques resulting in an emergent enriched micro-inertial homogenized continuum. This framework served as a basis for the semi-analytical analysis of LRAM designs [18] and allowed to construct computationally efficient multiscale techniques for large scale LRAM boundary value problems presenting a viable alternative to direct numerical simulations (DNS) [19].…”

Section: Department Of Mechanical Engineering Eindhovenmentioning

confidence: 99%

“…Next, the homogenized constitutive equations are derived through the sequential application of the localization and homogenization operators. First, the full scale displacement is approximated using the localization operator (19) as *…”

Section: The Homogenized Macro-scale Boundary Value Problemmentioning

confidence: 99%

Frequency domain boundary value problem analyses of acoustic metamaterials described by an emergent generalized continuum

2019

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This paper presents a computational frequency-domain boundary value analysis of acoustic metamaterials and phononic crystals based on a general homogenization framework, which features a novel definition of the macro-scale fields based on the Floquet-Bloch average in combination with a family of characteristic projection functions leading to a generalized macro-scale continuum. Restricting to 1D elastodynamics and the frequency-domain response for the sake of compactness, the boundary value problem on the generalized macro-scale continuum is elaborated. Several challenges are identified, in particular the non-uniqueness in selection of the boundary conditions for the homogenized continuum and the presence of spurious short wave solutions. To this end, procedures for the determination of the homogenized boundary conditions and mitigation of the spurious solutions are proposed. The methodology is validated against the direct numerical simulation on an example periodic 2-phase composite structure.

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“…lastic metamaterials (EMMs) have become an attractive research focus based on their unusual properties [1][2][3][4][5][6] . These specially designed composite structures have demonstrated a variety of intriguing effects and promising applications, including zero-index metamaterials (ZIM) 7,8 , wave transformation 9 , and negative refraction [10][11][12][13][14] .…”

mentioning

confidence: 99%

Topologically protected zero refraction of elastic waves in pseudospin-Hall phononic crystals

et al. 2020

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Zero-angle refraction of elastic waves in metamaterials has attracted attention for its extraordinary wave collimation properties. However, earlier implementations relied on the specific flat equifrequency curve of the phononic crystals suffer from a narrow range of incident angles or operating bandwidths, which severely hinders the exploration and design of functional devices. Here, we propose an elastic near-zero refractive index metamaterial of a triangular lattice to realize topological zero refraction with arbitrary angles of incidence and wide working frequency range. Topological robustness of the zero-angle refraction of pseudospin-Hall edge state against defects is experimentally demonstrated. Furthermore, tunable wave mode conversion associated with the zero-angle refraction is revealed and discussed. These results provide a paradigm for the simultaneous control of the refraction properties of longitudinal and transverse waves that can be employed for designing the topological elastic antennas and elastic wave collimator.

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

Cited by 45 publications

References 38 publications

A Review of Research on Seismic Metamaterials

A Review of Research on Seismic Metamaterials

Frequency domain boundary value problem analyses of acoustic metamaterials described by an emergent generalized continuum

Topologically protected zero refraction of elastic waves in pseudospin-Hall phononic crystals

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