6 th World Congresses of Structural and Multidisciplinary Optimization Rio de Janeiro, 30 May - 03 June 2005, Brazil An Inverse Method for Parameter Estimation in Active Laminated Structures Aur´ elio L. Ara´ ujo (1) ,Crist´ov˜ ao M. Mota Soares (2) , Jos´ e Herskovits (3) , Pauli Pedersen (4) (1) ESTIG - Polytechnic Institute of Bragan¸ca, Portugal aaraujo@ipb.pt (2) IDMEC - Instituto Superior T´ ecnico, Lisbon, Portugal cmmsoares@alfa.ist.utl.pt (3) COPPE - Federal University of Rio de Janeiro, Rio de Janeiro, Brazil jose@optimize.ufrj.br (4) Department of Mechanical Engineering, Technical University of Denmark, Lyngby, Denmark pauli@mek.dtu.dk 1. Abstract This paper addresses the problem of elastic and piezoelectric parameter estimation in active laminated structures with surface bonded sensors and actuators. The proposed technique is non destructive as the only experimental data it uses are natural frequencies of free vibration of the structure. Emphasis is placed on the influence on the estimated parameters of the adhesive material used to bond the piezoelec- tric patches to the laminate. The inverse problem is solved using the feasible arc interior point algorithm and an experimental application is described. 2. Keywords: Piezoelectric Properties, Optimization, Free Vibration, Adhesive Layers. 3. Introduction The use of most commercially available 2D numerical models along with the elastic, piezoelectric and dielectric properties provided by manufacturers does not guaranty sufficient accuracy for active control of noise and vibration in advanced applications such as those frequently encountered in the aerospace industry. During the last years several numerical models have been developed for simulation of active structures with piezoelectric sensors and actuators, both surface or embedded ones [1, 2]. The effect of the adhesive materials in the static or dynamic response in this type of structures has been studied experimentally [3] and numerical models that take into account the behavior and properties of the adhesive materials have been proposed [4, 5, 6]. For applications where the use of 2D plate or shell equivalent single layer numerical models is required, it becomes necessary to determine the properties of the different constituent materials that best predict the real behavior of the structure. This paper presents a non destructive method for estimation of material parameters of laminated active plates with surface bonded piezoelectric sensors and actuators. A finite element higher-order equivalent single layer numerical model which includes the piezoelectric effect [7] is used. The estimation of the material parameters is made by adjusting the response of the numerical model to the experimental response of the structure, consisting in a set of free vibration natural frequencies. Several techniques for the estimation of elastic properties of structures have already been presented by several authors. An assessment of the different approaches to the identification of mechanical properties based on free vibration response methods and optimization techniques in laminated plates is presented in [8]. Some methods that also use natural frequencies of vibration for estimation of elastic constants in composite material structures are based on surface response methods [9] and model updating techniques [10]. Another class of inverse methods combines wave propagation measurements with optimization techniques and, more recently, with genetic algorithms [11, 12]. Artificial neural networks were also used to solve this type of problems, based on wave propagation measurements [13] and also natural frequencies of free vibration for identification of elastic and piezoelectric parameters [14, 15]. As for the simultaneous identification of elastic and piezoelectric parameters in active structures using frequency response measurements, some methods have been presented [7, 14, 15, 16, 17]. This work is a generalization of a gradient based identification technique, which was originally de- veloped for multi-material laminated structures [18, 19, 20], and includes simultaneous identification of both elastic and piezoelectric properties [7, 14, 15]. The effect of the adhesive interfaces is studied with 1