Broadband wave attenuation using periodic membrane-frame structures

This study numerically and experimentally investigates the propagation characteristics of flexural waves in metamaterial beams with periodic membrane-frame structures. The interior membrane-frame structure acts as a local resonator. As the wave frequency is close to the resonant frequency of the membrane-frame structure, most of the energy produced by disturbances can be absorbed by the interior substructure, resulting in a ceasing motion in the host beam. Owing to such locally resonant mechanism, bandgaps where no wave can propagate freely are created. By altering frame mass magnitude, frame width, and position, the bandgap location can be easily tailored. In comparison with a concentrated mass of the same weight, the frame mass is more efficient in producing a broad frequency band with strong wave attenuation. The study on effective mass density is also carried out to reveal the bandgap mechanism. The resonant-type bandgap coincides with the frequency range of negative effective mass density. As the effective mass density becomes negative, the acceleration of the host beam and applied loading are in the opposite direction. The out-of-phase motion between the acceleration and applied loading results in a decay in amplitude. Adding an extra mass to the membrane-frame structure can achieve multiple bandgaps. Vibration experiments are conducted to verify finite element (FE) predictions.