: Hirsekorn, S.; Gebhardt, E.; Arnold, W.

Abstract
A simple physical model of 1-3 piezoelectric composites can be used to determine the material properties that are relevant to thickness-mode oscillations. If the lateral scale of the composite is sufficiently fine, it can be treated as an effective homogeneous medium. This model is extended to graded 1-3 composites in which the diameter and (or) the number of the piezoelectric ceramic rods is varied in through thickness direction to allow broadband thickness oscillations. If the lateral scale is sufficiently fine over the thickness, the graded composite can be described as a stack of homogeneous layers of different material properties. The frequency dependent oscillatory behavior of graded 1-3 composite transducers including backing, matching layers, and feedback effects of the voltage source is calculated analytically. The equations obtained are numerically evaluated and compared with experimental results. Objective of this work are design and optimization criteria for the constructio n of graded piezoelectronic composites for applications.