Bandgap and mode shape tuning of piezoelectric metamaterial

Abstract

The mode shape of piezoelectric metamaterials is tuned by manipulating spatially the electrical boundary conditions of the piezo-elements, in a desired and controlled manner, in order to tailor the wave propagation characteristics through these metamaterials. The proposed concept relies on the fact that open-circuit piezo-elements made of lead-zirconate-titanate (PZT4) are twice as stiff as the same piezo-elements when operating under short-circuit conditions. Appropriate switching of the boundary conditions of the different piezo-elements between open and short-circuit conditions results in any desirable spatially distribution of the stiffness over the entire metamaterial volume. With such capabilities, it would be possible to control the bandgap characteristics of the metamaterial. But, more importantly, it would also be feasible to alter the mode shape characteristics of the metamaterial in order to control the magnitude and direction of wave propagation. This in effect enables controlling or breaking the reciprocity characteristics of the metamaterial. A finite element model (FEM) is developed to model the bandgap and mode shape characteristics of one-dimensional piezo-metamaterial. The effect of various switching strategies on the location and spectral width of the bandgap characteristics is illustrated. Furthermore, the switching strategies are also shown to influence the mode shapes, energy flow, and reciprocity characteristics of the piezo-metamaterial.