This paper is concerned with the detailed analysis of the behavior of a piezoceramic bi-morph torsion actuator using the d 15 -effect. The bi-morph actuator is made of two oppositely polarized adjacent piezoceramic prismatic beams. The mathematical analysis is based on the Saint-Venant torsion theory; a formulation of the electromechanically coupled problem in terms of a stress function and of the electric potential is derived, which represents an exact solution of a specific three-dimensional problem; in particular, for the case when the axial stress and the axial component of the electric displacement vector are independent of the axial coordinate. The resulting boundaryvalue problem in the cross-section is solved using the method of finite differences. Solutions for the actuated rate of twist are presented and compared to three-dimensional electromechanically coupled finite element solutions using ABAQUS ® for the case of a cantilevered bi-morph actuator. A very good agreement is found.
IntroductionStructures that integrate sensors and actuators into load-bearing structures by means of multi-functional materials like, e.g. piezoelectric materials, are usually denoted as smart or intelligent structures; see Crawley [1] or Chopra [2] for reviews. In combination with active and passive control strategies smart structures have applications in the fields of vibration damping, noise reduction, shape control, structural and health monitoring, and so on; see, e.g. Rao and Sunar [3].A piezoelectric material subjected to an electric field is mechanically deformed; conversely, a mechanical deformation results into an electric field. This behavior can be used to put piezoelectric actuators and sensors into practice. The actuator effect is denoted as the converse piezoelectric effect and the sensor effect as the direct piezoelectric effect; see Mason [4] or Yang [5]. In the following, the actuating piezoelectric strains are considered as mechanical eigenstrains, a generalized notion introduced by Mura [6] in order to describe incompatible parts of strain, such as thermal, plastic misfit as well as piezoelectric strains. In analogy, the sensing effect has been formally accounted for by means of a so-called