No abstract

Piezoelectric plates have been widely used for the vibration reduction and noise control of structures. Due to power forces considerations, electrostrictive patches present a growing interest. It is thus the purpose of the present research to contribute to modeling aspects of thin structures integrating such actuators. Many three-dimensional finite element models have then been elaborated to simulate these structures behavior but no two-dimensional models have been presented up to now. The aim of this article is thus to set out the elaboration of a thin plate electrostrictive finite element for PMN-PT type ceramics used as actuators. This element is developed for dynamic purposes and thus takes into account phenomena induced by applying to the patch a cycling electric field. The finite element formulation is based on electromechanical constitutive equations derived in a previous paper, mechanical and electrical considerations and direct a priori plate assumptions. The electrostrictive finite element is here derived using techniques inspired from a piezoelectric finite element. This method has the particular property of reducing the initial electromechanical problem to a purely mechanical problem based on a modified elastic constitutive law. The electrical unknowns are then explicitly derived from the mechanical displacements. This method considerably simplifies the resolution of the problem since classical finite elements for laminated plates can be used to model the electrostrictive plate with a modified constitutive law. This paper is focused on the plate modeling and corresponding variational formulations.

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.

The aim of this work is to develop a simple and very efficient tool, to simulate the active control of laminated plates, and in a next step, to optimize the geometry and number of sensors and actuators. A new piezoelectric Finite Element is presented. It is an eight node plate with one electrical potential degree of freedom for each interface of piezoelectric layers. The usual FSDT theory is combined with a "field compatibility" methodology to avoid the transverse shear locking for thin plates. A LQR control method including a state observer is used to compute the control. Four examples are presented. The quasi-static correction and the use of collocated sensor/actuator are discussed.

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.