Abstract
Vibration band gaps and elastic wave propagation are examined in the metamaterial plates manufactured with periodic locally resonant membranes arranged in a square array. Periodic metamaterials exhibit unique dynamic characteristics stemming from their ability to act as mechanical filters for wave propagation. As a result, waves propagate along the periodic cells only within specific frequency bands called the pass bands, while being blocked within other frequency bands called the stop bands. The proposed metamaterial plates are equipped with sources of local resonances which act as local absorbers of mechanical vibrations. The macroscopic dynamical properties of the resulting periodic structures depend on the resonant properties of substructures which contribute to the rise of interesting effects such as broad stop band characteristics that extend to lower frequencies. Externally excited piezoelectric polyvinylidene difluoride membranes are used to support the local resonators. The stiffness of the piezo-membranes is tunable by means of an external voltage allowing us to control the location and bandwidth of the local resonance frequencies. The predicted band structures are validated by investigating the frequency response of the plate to external mechanical excitations using a comprehensive finite element model of the entire structure. By examining the proposed metamaterial plate, it is shown that it would be possible to actively control the wave propagation both in the spectral and spatial domains in an attempt to steer, stop, and/or confine the propagation of undesirable external disturbances.