Bandgap, dispersion, and non-reciprocal characteristics of an active Willis metamateriala)

Active Willis metamaterials (AWM) have attracted considerable attention, recently, by virtue of their unique electro-elastic coupling, controllability, and observability characteristics. In this paper, these characteristics are utilized to further demonstrate other unique bandgap, dispersion, and non-reciprocal capabilities that distinguishes them from conventional materials. A one-dimensional example of a piezoelectric-based AWM is presented to demonstrate the tunability of the bandgap and dispersion characteristics during forward and backward propagations. In the selected example, the AWM consists of two dissimilar masses connected by a piezoelectric spring. Lagrange dynamics approach is employed to develop the equations governing the Willis coupling, the piezoelectric coupling, and to reveal the inherent control abilities of the bandgap and dispersion characteristics. With this developed controlled-based structure of the AWM, it is shown that the AWM can simultaneously monitor and control both the physical properties as well as spatial width and the spectral location of the bandgaps while controlling the wave number and acoustical impedance at specific desirable levels. It is envisioned that the developed simple one-dimensional AWM model has revealed more interesting wave propagation and control capabilities which can help investigating more complex configurations of the AWM's.