Analytic model of phononic crystals with local resonances

Liu, Zhengyou; Chan, Che Ting; Sheng, Ping

doi:10.1103/physrevb.71.014103

Cited by 460 publications

(297 citation statements)

References 6 publications

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“…Subsequently, in Ref. 5, an analytic model was constructed to show that around the locally resonant frequencies, the effective mass density of the LRSM is negative, thus providing the first support to the fact that effective dynamic mass density can be not only different from, but also opposite in sign from the static mass density. However, that still leaves open the question: Are the conclusions of Kuster and Toksöz and Berryman correct in the limit of zero frequency?…”

Section: Recapitulationmentioning

confidence: 99%

Effective dynamic mass density of composites

et al. 2007

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The static mass density of a composite is simply the volume average of its constituents' densities. The dynamic density of a composite is defined to be the quantity that enters in evaluating the elastic wave velocity at the low-frequency limit. We show through a rigorous derivation that the effective dynamic mass density of an inhomogeneous mixture can differ from its static counterpart when the composite matrix is a fluid or, more generally, when there are relative motions between the matrix and inclusions. Derivation of the dynamic mass density expressions, involving taking the long wavelength limit of the rigorous multiple scattering theory, is detailed for the two-dimensional case. We also extend the effective dynamic mass density expression to finite frequencies where there can be low-frequency resonances. By combining both analytical and numerical approaches, negative or complex dynamic mass density is obtained for composites that contain a sufficient fraction of locally resonant inclusions. Thus, the dynamic mass density of a composite can differ from the static ͑volume-averaged͒ value even in the zero frequency limit, although both must be positive in that limit. Negative or complex dynamic mass density can occur at finite frequencies. These two results are shown to be consistent with each other, as well as related by the same underlying physics. As by-products of our rigorous derivation, we also verify some prior known results on the effective elastic moduli of composites.

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Section: Recapitulationmentioning

confidence: 99%

Effective dynamic mass density of composites

et al. 2007

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“…The LRSMs were usually composed of three types of materials, forming a stiff/flexible/stiff structure [27]. To further study the locally resonant absorption mechanism, we compare materials by removing one of component materials to break the stiff/flexible/stiff structure.…”

Section: Resultsmentioning

confidence: 99%

Investigation of locally resonant absorption and factors affecting the absorption band of a phononic glass

et al. 2014

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We experimentally and theoretically investigated the mechanisms of acoustic absorption in phononic glass to optimize its properties. First, we experimentally studied its locally resonant absorption mechanism. From these results, we attributed its strong sound attenuation to its locally resonant units and its broadband absorption to its networked structure. These experiments also indicated that the porosity and thickness of the phononic glass must be tuned to achieve the best sound absorption at given frequencies. Then, using lumped-mass methods, we studied how the absorption bandgaps of the phononic glass were affected by various factors, including the porosity and the properties of the coating materials. These calculations gave optimal ranges for selecting the porosity, modulus of the coating material, and ratio of the compliant coating to the stiff matrix to achieve absorption bandgaps in the range of 6-30 kHz. This paper provides guidelines for designing phononic glasses with proper structures and component materials to work in specific frequency ranges.

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“…Low-frequency spectral gaps were noticed by Zhikov [47,48]. Negative effective mass densities, due to local resonances, were discovered in 2000 [49], although it was not until later that the experiments were correctly interpreted [50]. In periodic arrays of split cylinders, negative magnetic permeability can be related to the negative effective mass density in antiplane vibrations, due to the fact that both are governed by the Helmholtz equation [51].…”

Section: To Ananya and Krishna To Alaa And Ismailmentioning

confidence: 99%

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2017

Dynamics of Lattice Materials

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Analytic model of phononic crystals with local resonances

Cited by 460 publications

References 6 publications

Effective dynamic mass density of composites

Effective dynamic mass density of composites

Investigation of locally resonant absorption and factors affecting the absorption band of a phononic glass

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