The dynamic behaviour of interacting piezoelectric actuators in smart structures

The concept of using a network of piezoelectric actuators and sensors to form a self controlling and self monitoring smart system in advanced structural design has drawn considerable interest among the research community. The behaviour of these smart structures is governed by the shape, size and distribution of piezoelectric actuators/sensors. However, the problem is even more complicated by the fact that these smart structures are generally characterized by electromechanical coupling, the presence of inhomogeneities and interfaces. It is with this in mind that the current research program was undertaken. Four aspects of the work were accordingly examined. The first was concerned with the development of an analytical model capable of predicting the dynamic local stress field around a piezoelectric actuator. The theoretical formulations are based upon the use of Fourier transform, which reduce the original problem into the solution of integral equations in terms of the interfacial stresses of the actuator. The resulting integral equations are then solved using Chebyshev polynomial expansions. The significance of this newly developed analytical model is manifested by its versatility and application to different geometries, material combinations and loading frequencies. This model can also treat quasistatic loading conditions. The second was concerned with the development of a general theoretical method, pseudo-incident wave method, for the evaluation of the interaction between actuators in smart structures. The theoretical formulations are based upon the use of a consistent superposition procedure, which reduces the original interaction problem into the solution of a set of coupled single actuator problems. By using the single actuator solution, as the building block, this newly developed method provides a general approach to deal with interacting actuators involving complex boundary/interfacial conditions. The third was concerned with examining the effect of interacting microdefects upon the local stress field. In this case, the newly developed pseudo-incident wave method was extended to crack problems, with the single crack solution being the fundamental solution. The effect of the location of the cracks, the material properties and the loading frequency upon the local stress field is examined and discussed. The fourth was concerned with the experimental verification of some aspects of the developed quasistatic and dynamic models. In the static case, the local stress field at the ends of an actuator was simulated using photoelasticity. In the dynamic case, cantilever beams containing bonded piezoceramic actuators and sensors were tested using an inverter drive circuit. The frequency response of these beams as a result of the presence of these actuators and sensors was measured and compared with the theoretical predictions. The results reveal good agreement between the two. Furthermore, the work considered the use of multiple actuators and sensors to suppress the vibration of a smart beam. The results of the present investigation reveal that the local stress field around an actuator and, consequently, the load transfer are dramatically influenced by the material combination, the geometry of the actuator and the loading frequency. They also show that the load transfer between the actuator and the host structure can be reliably predicted using the newly developed actuator model. Finally, the results indicate that the interaction between actuators may significantly influence both the local and global behaviour of smart structures.