Abstract
In this paper, we demonstrate the consequence of using different equivalent models to represent a lattice system consisting of mass-in-mass units and why negative mass is needed in the equivalent model. Dispersive wave propagation in the lattice system is studied and compared to various equivalent models. It is found that, if the classical elastic continuum is used to represent the original mass-in-mass lattice system, the effective mass density becomes frequency dependent and may become negative for frequencies near the resonance frequency of the internal mass. In contrast, if a multi-displacement microstructure continuum model is used to represent the mass-in-mass lattice system, the dispersive behavior of wave propagation and the band gap structure can be adequately described. However, while the acoustic mode is accurately described by the microstructure continuum model, the description of the optical mode is accurate only for a limited frequency range.
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