Design of Actuator Networks for Dynamic Displacement Tracking of Beams

Abstract

Adaptive and smart structures have become a major subject of contemporary research. Smart structures are structures that—like human beings—are capable of automatically reacting to disturbances exerted upon them by the environment they are operating in. Typically, smart structures are put into practice by embedding or attaching smart materials to a substrate structure. These materials have both actuating and sensing capabilities; a popular example would be piezoelectric materials that exhibit the direct and the converse piezoelectric effect. As many of the structures, which are considered as candidates for implementing smart materials, are continuous structures, there is an inherent need for properly distributing the actuation as well as the sensing. A method that has been successfully utilized for the design of distributed actuators is shape control. In general, shape control is concerned with finding a distributed actuation such that a structure assumes a desired shape. The latter shape may be the undistorted shape of the structure, despite the action of external disturbances, or it may be a prescribed new shape for the structure. In the present paper we consider the case of the structure taking on a prescribed shape; i.e., we present a method for finding distributed actuators or dense actuator networks such that a desired displacement field is tracked. We use eigenstrain type actuators for that sake. In the first part we discuss dynamic deflection tracking of beams by distributed actuation, and in the second part we focus on the use of dense networks of actuator patches with a section-wise constant intensity to approximate the effectiveness of the distributed actuators. In the example problem we assume the actuator patches made of piezoelectric materials, taking into account the mass and stiffness of the patches as well as the electromechanical coupling due to the direct piezoelectric effect. The efficiency of the presented method is clearly demonstrated by the latter study.