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International audience; In this article, the active vibration control of a smart structure made out of a single functionally graded piezoelectric material layer, equipped with a network of discrete electrodes, is studied. The material properties vary continuously across the direction of thickness, so that top and bottom surfaces consist of pure PZT4 and the mid surface is composed of pure aluminium. The percolation phenomenon is taken into account. A functionally graded piezoelectric material plate finite element based on the first-order shear deformation theory hypothesis and layer-wise approximation for electric potential is implemented. An optimization procedure is considered to define the relevant electrodes for actuators and sensors, based on controllable and observable criteria. An adaptative fuzzy controller system is used, activating with relevance the actuators according to the most excited eigenmodes. Simulations show the effectiveness of this kind of concept.

In this paper, the active vibration control tools are implemented for the vibration control of functionally graded material (FGM) beam with piezoelectric actuators and sensors. The properties of FGM are functionally graded in the thickness direction according to the volume fraction power law distribution. An analytical formulation, based on an efficient trigonometric shear deformation theory, is used to obtain a state space equation. The main steps to set up active control of FGM vibrations are considered in this work. The actuators’ and sensors’ locations are defined from two optimization problems using controllability and observability gramians. The linear quadratic regulator (LQR) control law, including a state observer is computed. Numerical examples show the influence of the volume fraction index on the observability and controllability properties of the system. The LQR leads to efficient active damping for several kinds of excitations. The study of the uncertainty in the volume fraction index shows the robustness of the control method, and also the possible induced defects.

This study presents a novel finite element (FE) for shell structures including piezoelectric actuators and sensors. Based on a conventional 8-node shell formulation and the classical displacement-based variational formulation, the present element has an enriched description of the transverse kinematics in order to consistently retain the full three-dimensional (3D) piezoelectric coupling. Furthermore, a layer-wise description of the electric degrees of freedom permits to account for embedded piezoelectric actuators and sensors. The robustness of the FE is enhanced by referring to an established technique that avoids transverse shear locking and membrane locking. Numerical results are given which validate the present implementation and highlight the efficiency and accuracy of the proposed formulation. Additionally, some new reference solutions for the static behavior of piezoelectric shells are provided by means of 3D FE computations with a commercial software.

An original piezoelectric plate theory has been presented in the companion paper (Osmont and Pablo, 2008). The particularity of the ‘piezoelectric’, finite element stemming from this theory lies in the fact that no electric degree of freedom is needed to take into account the electromechanical coupling. This article is focused on the validation of this theory through various benchmarks issued from literature. It will be proved that results are in quite agreement with static and dynamic reference solutions of laminated composite plates equipped with piezoelectric patches.

Several studies have been conducted in order to find the optimal location of actuators and sensors in the active vibration control of structures. In this paper, a modified optimization criterion is proposed for these two optimization problems, ensuring good observability or good controllability of the structure, and considering residual modes to limit the spill-over effects. Its efficiency is shown by the comparison with the classical criteria, illustrated for a simply supported beam and a rectangular plate. In these two applications, the number of active elements is discussed, using or neglecting the residual modes.