An impact based mass-in-mass unit as a building block of wideband nonlinear resonating metamaterial

Vibration transmission through a mass-in-mass unit is frequency dependent due to the difference in phase between the internal resonator and the surrounding structure. Generally, the attenuation band is confined between the two-transmission bands for a linear resonating metamaterial. In the case of a linear metamaterial, the attenuation band can be widened up to a certain limit by tuning the material properties, but cannot be extended infinitely by removing the 2nd transmission band. An impacting resonator can attenuate the vibration of the metamaterial due to the counteraction of the external excitation by the resulting impulse force and due to the presence of the sub and super-harmonic and chaotic responses. This paper theoretically elucidates that an impact metamaterial can results zero averaged effective mass for the multi-periodic type impacting vibration as in these frequency ranges vibration becomes essentially out of phase. Most importantly, an impacting metamaterial has a potential to extend the attenuation bandwidth by reducing the vibration of the main structure even for the minimal mass ratio. The scope of the paper is limited to analysis of a single building block of the impacting metamaterial to provide better insight comprehension of the effect of impacting oscillation inside a metamaterial unit more systematically.