Localization of electro-elastic shear waves in a periodically stratified piezoelectric structure

Abstract

We investigate the localization of electro-elastic shear waves travelling along a homogeneous piezoelectric superlattice waveguide with thin electrodes periodically inserted parallel to the waveguide faces. The transfer matrix between two neighbouring sub-layers is constructed based on the electrically shorted conditions on the electrodes. A relationship is established between elastic displacements of the top and bottom faces of the superlattice when these faces are traction free. When they are clamped a relationship is established between tangential stresses on the two faces. It is shown that due to the electro-mechanical coupling, waves can be localized at interfaces in the structure if the electrodes are non-uniformly distributed along the thickness of the piezoelectric waveguide. The localization of waves significantly increases with the number of non-symmetrically introduced electrodes between the layers. The results of the paper can be helpful in the design of narrow band filters or multi-channel piezoelectric filters.