Keywords: inverse problems, active structures, mechanical material properties, piezoelectric material properties.

The need for accurate elastic, piezoelectric and damping parameters in the modelling and analysis of active laminated plate type structures has become a major concern in active control applications. Traditional estimates based upon engineering tables provided by manufacturers are not always reliable for these applications, as a result of the substantial variability among samples, dynamic ranges of interest and, more importantly, when different materials are combined as components in an active composite material configuration, the effective values of material parameters are usually found to be quite different. In fact, the use of most commercially available two-dimensional numerical models along with the elastic, piezoelectric and damping properties provided by manufacturers does not guarantee sufficient accuracy for the active control of noise and vibration in advanced applications such as those frequently encountered in the aerospace industry.

In response to these difficulties, one can estimate some of these unknown parameters through non-destructive experiments with the physical structure. The general idea is to be able to determine the effective properties in an in-service part with the purpose of updating an analytical or numerical model that describes the behaviour of the structure and that will be used in applications for response prediction, control and monitoring. This is usually done using experimentally measured data types that can also be obtained through the analytical or numerical model, and the associated inverse problem can be solved in a number of different ways.

This chapter presents a survey on inverse techniques for identification of mechanical and piezoelectric properties in laminated adaptive structures with integrated piezoelectric sensors and actuators. The major part of the chapter is devoted to the inverse methods for characterisation of elastic properties, which have a somewhat greater expression in the literature. Several techniques were considered, such as those based on inverse eigenvalue problems, full-field and wave propagation techniques. The identification of piezoelectric properties in the context of active structures, i.e. simultaneous identification of elastic and piezoelectric properties, was found to have relatively little expression in the literature, although the results presented by the few authors that have developed work in this field show that the identified properties can be quite different from the ones reported by individual manufacturers. As damping behaviour can also be of interest in the context of composite materials, the chapter also includes a brief survey on inverse methods for identification of hysteretic damping.

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