On the negative effective mass density in acoustic metamaterials

Veselago, 1968, The electrodynamics of substances with simultaneously negative values of ε and μ, Sov. Phys. Usp., 10, 509, 10.1070/PU1968v010n04ABEH003699 Pendry, 2000, Negative refraction makes a perfect lens, Phys. Rev. Lett., 85, 3966, 10.1103/PhysRevLett.85.3966 Valentine, 2008, Three-dimensional optical metamaterial with a negative refractive index, Nature, 455, 376, 10.1038/nature07247 Li, 2004, Double-negative acoustic metamaterial, Phys. Rev. E, 70, 055602, 10.1103/PhysRevE.70.055602 Fang, 2006, Ultrasonic metamaterials with negative modulus, Nat. Mater., 5, 452, 10.1038/nmat1644 Ding, 2007, Metamaterial with simultaneously negative bulk modulus and mass density, Phys. Rev. Lett., 99, 093904, 10.1103/PhysRevLett.99.093904 Cheng, 2008, One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus, Phys. Rev. B, 77, 045134, 10.1103/PhysRevB.77.045134 Chan, 2006, On extending the concept of double negativity to acoustic waves, JZUS A, 7, 24, 10.1631/jzus.2006.A0024 Liu, 2000, Locally resonant sonic materials, Science, 289, 1734, 10.1126/science.289.5485.1734 Liu, 2005, Analytic model of phononic crystals with local resonances, Phys. Rev. B, 71, 014103, 10.1103/PhysRevB.71.014103 Milton, 2007, On modifications of Newton’s second law and linear continuum elastodynamics, Proc. R. Soc. A, 463, 855, 10.1098/rspa.2006.1795 Lazarov, 2007, Low-frequency band gaps in chains with attached with non-linear oscillators, Int. J. Non-linear Mech., 42, 1186, 10.1016/j.ijnonlinmec.2007.09.007 Vincent, 1898, On the construction of a mechanical model to illustrate Helmholtz’s theory of dispersion, Philos. Mag., 46, 557, 10.1080/14786449808621232 Yao, 2008, Experimental study on negative mass effective mass in a 1D mass-spring system, New J. Phys., 10, 043020, 10.1088/1367-2630/10/4/043020 Cosserat, 1909 Sun, 2007, Modeling heterogeneous media with microstructures of different scales, J. Appl. Mech., 74, 203, 10.1115/1.2188536 Huang, 2007, Continuum modeling of solids with micro/nanostructures, Philos. Mag., 87, 3689, 10.1080/14786430701400137 Sheng, 2003, Locally resonant sonic materials, Physica B, 338, 201, 10.1016/S0921-4526(03)00487-3 Brillouin, 1953 I.A. Kunin, Elastic Media with Microstructure I & II, Springer-Verlag, Berlin, Heidelberg, New York, 1982–1983.