Sat, 26 Jul 2008 13:42:04 BST CiteULike: norris Sheng http://www.citeulike.org/user/norris/author/Sheng CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/norris/article/2038137 <i>Physical Review B (Condensed Matter and Materials Physics), Vol. 76, No. 13. (2007)</i><br /><br />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-averaged) 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. Effective dynamic mass density of composites Jun Mei Zhengyou Liu Weijia Wen Ping Sheng doi:10.1103/PhysRevB.76.134205 Physical Review B (Condensed Matter and Materials Physics), Vol. 76, No. 13. (2007) 2007-12-01T16:32:44-00:00 2007 Physical Review B (Condensed Matter and Materials Physics) 76 13 APS metamaterial http://www.citeulike.org/user/norris/article/1172258 <i>Physical Review B (Condensed Matter and Materials Physics), Vol. 71, No. 1. (2005)</i><br /><br />A simple analytic model is presented to describe the low-frequency effective mass densities of three-component phononic crystals with local resonances. We show that the effective mass densities can turn negative close to the local resonances. Expressions for the effective mass densities are derived for both three-dimensional systems with coated spheres embedded in a host matrix, and two-dimensional systems with coated cylinders embedded in a host matrix. Analytic model of phononic crystals with local resonances Zhengyou Liu CT Chan Ping Sheng doi:10.1103/PhysRevB.71.014103 Physical Review B (Condensed Matter and Materials Physics), Vol. 71, No. 1. (2005) 2007-03-18T22:45:32-00:00 2005 Physical Review B (Condensed Matter and Materials Physics) 71 1 APS phonons