Heterogeneous structures with negative effective mass

Dynamic mass of a composite is different from the gravitational one; careful placement of mass elements in the composite may result in resonance under wave loading. This resonant effect will induce negative effective mass, which has a substantial effect on the overall behavior of the composite. We first study the lattice wave propagation in a discrete mass-spring system, where mass-in-mass structures are connected by elastic springs. Around the resonant frequency, composite units are demonstrated both by theoretical and experimental methods to have negative effective mass, leading to anomalous dispersion effect. Its counterpart in continuum materials is the epoxy matrix filled with rubber-coated lead spheres, where effective mass of such a composite is shown to be negative near the resonant frequency, due to the out-of-phase motion of heavy inclusions in the composite. When the inner mass is clamped, negative effective mass is found to take place in the band below a critical frequency. For a two dimensional waveguide with rigid clamped boundary, it can be homogenized as a material with negative mass following the Drude relation. These findings will have potential applications in low-frequency noise barriers and vibration dampers.