Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density

The wave attenuation and energy transfer mechanisms of a metamaterial having a negative effective mass density are studied. The metamaterial considered is represented by a lattice system consisting of mass-in-mass units. The attenuation of wave amplitude for frequencies in the stop band is studied from the energy transfer point of view. It is found that most of the work done by the external force on the lattice system is stored by the internal mass if the forcing frequency is close to the local resonance frequency. However, the energy stored in the internal mass is only temporary; it is taken out by the external force in the form of negative work in a cyclic manner. This behavior is utilized to design metamaterials for preventing stress waves from passing them.