Vibration confinement of thickness-shear and thickness-twist modes in a functionally graded piezoelectric plate

We analyze shear-horizontal vibrations of a functionally graded piezoelectric plate of polarized ceramics or crystals of 6mm symmetry. The material of the central portion of the plate is different from that of the rest of the plate. It is shown that when the material properties of the central portion and the rest of the plate satisfy certain conditions, there exist trapped thickness-shear and thickness-twist modes whose vibrations are mainly confined within the central portion and decay quickly outside the central portion. The effects of the functionally graded material properties on the behaviors of the trapped modes are examined.