Metamaterials are materials with manmade microstructures. Recently, researchers have looked at a class of metamaterials whose microstructures contain internal degrees of freedom that are different from those of the macro-medium. These metamaterials exhibit unusual dynamic behavior and if modeled as homogeneous solids then their effective mass densities would become negative in certain frequency range. Specifically, a new stop band in the vicinity of the local resonance frequency of the internal mass in the microstructure would result. In this paper, a one dimensional metamaterial is employed to investigate the meaning of the negative mass density in the material and the energy flow in and out of the microstructure. In addition, numerical solutions are used to illustrate the phenomenon.

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