Several studies have been developed in order to find the optimal location of actuators and sensors in active control of structures. In this paper, a modified optimization criteria is proposed for these two optimization problems, ensuring good observability or good controllability of the structure, and considering residual modes to limit the spillover effects. Its efficiency is shown by comparison with 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.

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SUMMARYThis paper presents a method for a quick evaluation of stresses and displacements in a plate structure for elastostatic problems. First, an approximation is built from the mathematical structure of the solutions for starshaped domains, which is representative of long wavelength effects. Second, a variational formulation consistent with this approximation is proposed. Finally, two alternative procedures for coupling adjacent domains are demonstrated.

The control of complex structural models is a eld of growing interest. The problem studied herein concerns damping updating using experimental frequency response functions. Although there are several methods improving structural dynamic models, only a few of them deal speci cally with damping improvements. The method introduced is built on mechanical bases, using an error measure on the constitutive relations. The tuning strategy uses an iterative process, each iteration consisting of two steps. The rst one is the localization of the erroneous regions. The second step is the correction of the parameters belonging to these regions. Examples illustrate the sensitivity of the error to the damping defects and its effectiveness for updating damped structures. Nomenclaturea = damping tensor <. / = real part " = strain tensor ¾ = stress tensor f g = column (dimension n) Subscripts a = magnitude ad = admissible quantity c = kinematical quantity d = imposed quantity E = substructure E s = statical quantity sym = symmetric ! = frequency-domain quantity Superscripts ¤ = conjugate and transpose .Q/ = experimental quantity

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.