These methods can be more efficient than traditional test methods in the sense that they rely on global system response measurements like natural frequencies of free vibration, eliminating the problem that often arises when measuring inhomogeneous strain fields with strain gauges [1]. Also, for dynamic applications like active control, properties may vary with the frequency range of interest, being the present methods capable of predicting in a more accurate way those variations. Finally, the proposed techniques can be applied to the real structure, accounting for the real material parameters arising from the combination of the different composite and piezoelectric materials, where very often the gluing material that bonds the surface sensors and actuators to the underlying structure is not taken into account in the model.

A higher order laminated plate model which incorporates the piezoelectric effect has been developed for the purpose of this parameter estimation along with an eight nodded serendipity plate element with nine mechanical degrees of freedom per node and one electric degree of freedom per element [2]. This numerical model allows the identification of six elastic parameters and two piezoelectric coefficients per material.

The first of the proposed methods uses gradient based optimization in order to solve the inverse problem, minimising a weighted least squares type error function, which expresses the difference between a set of natural frequencies produced by the numerical model and the experimentally obtained ones. This defines a constrained non linear optimization problem, due to the need to ensure positive definiteness of the elasticity matrices for all materials. The problem is solved by a non linear interior point algorithm (FAIPA - Feasible Arc Interior Point Algorithm) [3], using analytical sensitivities.

Instead of solving the inverse problem in an iterative way, the alternatively proposed method builds a metamodel of the inverse problem, using artificial neural networks. In this approach the network is trained using a data set produced by the numerical model, which consists of pairs of sets of natural frequencies (inputs) and properties (outputs). The dimension of this data set is substantially reduced using the concept of orthogonal arrays, while preserving all meaningful information for supervised training purposes.

An application is presented, where the elastic parameters of a carbon T300 laminated plate are identified based on experimentally measured natural frequencies and the identification of the elastic and piezoelectric properties of a set of nine pairs of collocated PZT-5J patches is simulated. The comparison of the results produced by the two methods show excellent agreement with each other and with the goal properties in the simulations, suggesting some potential for practical applications.

1

P. Pedersen, "Identification techniques in composite laminates", In: C.A. Mota Soares, C.M. Mota Soares, M.J.M. Freitas, editors, Mechanics of Composite Materials and Structures, Dordrecht: Kluwer Academic Publishers, 443-452, 1999.

2

A.L. Araújo, C.M. Mota Soares, J. Herskovits, P. Pedersen, "Development of a finite element model for the identification of mechanical and piezoelectric properties through gradient optimisation and experimental vibration data", Composite Structures, 58, 307-318, 2002. doi:10.1016/S0263-8223(02)00192-7

3

J. Herskovits, V. Dubeux, C.M. Mota Soares, A.L. Araújo, "Interior point algorithms for nonlinear constrained least squares problems", Inverse Problems in Science and Engineering, 12(2), 211-223, 2004. doi:10.1080/10682760310001598698

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