A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures

The main objective of this article is to present an overview of the modelling that has been proposed by various workers in the field of smart or intelligent structures. Before the main discussion on the various models, some background information will be presented in relation to intelligent structures and the types of adaptive materials that are available. Although there are several categories of materials that can be implemented in intelligent structures, this article will focus on models that use piezoelectric materials as sensors and/or actuators (S/A). The modelling of the intelligent structures can be categorised in terms of the structural configuration (e.g., rod composites, fibre composites, monolithic structures, etc.) and also according to the type of modelling whether by finite element modelling or by analytical exact solutions. Models in this field of work had incorporated concepts from different background including three-dimensional linear elastic theory and dielectric theory to give rise to the linear piezoelectric model. Rules of Mixture and methods for calculating effective properties of fibre composites were extended to include piezoelectric fibre composite models. Classical Laminated Plate Theory was also adopted in laminated composite models where some laminae were piezoelectric materials. Exact solutions were applied to simple models and illustrated the potential of using piezoelectrics. Finite element techniques were used for more complicated problems that included complex geometries, nonlinear behaviour and dynamic control of the structure. The difference between induced strain and actuation strain is usually not addressed when using FE techniques, instead the piezoelectric strain can be regarded as an equivalent external force/moment or incorporated into the strain energy. In regard to control algorithms, the most common form applied by investigators in this field seems to be the negative velocity feedback control with single input and single output and some included linear quadratic control. More advanced control algorithms such as using multiple input and multiple output or even neural networks are less established.