In active vibration control of smart structures, the actuator and sensor placement is a key point of the control system design. Even the most robust control logics could easily make a structure unstable if the actuators and sensors were not correctly positioned. The objective of this paper is to propose an H2 norm approach for the actuator and sensor placement. Unlike most modal H2 norm actuator and sensor placement methodologies, this work aims not only to maximize the norms of the controlled modes but also to reduce spillover problems by taking into account the residual modes and minimizing their H2 norms. It discusses the optimal actuator and sensor configuration in a finite element model of a square plate fixed on three sides with piezoelectric patch actuators and acceleration sensors. Finally, downstream of the actuator and sensor positioning, IMSC, PPF and NDF controls have been tested and discussed.

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In general active vibration control intrinsically implies a fatigue damage reduction. Anyway, this assumption is not always verified. In these cases it is possible to deeper investigate the fatigue phenomena on smart flexible structures and their reduction from a control point of view. In this article, to identify the problem main parameters, a simplified interpretation of fatigue damage is given using the frequency analysis framework. Then, the active control logic is defined as an optimization problem with a quadratic functional taking into account the previously cited parameters. Finally, because of non-linearity of fatigue phenomenon, an adaptive approach is applied and a numerical/experimental validation is carried out. © 2013 SPIE

We carry on the investigation started in [2] about the regularity of weak solutions to the strongly degenerate parabolic equationwhere Ω is a bounded domain in R n for n ≥ 2, p ≥ 2 and ( • ) + stands for the positive part. Here, we weaken the assumption on the right-hand side, by assuming that f ∈ L p ′ loc 0, T ; B α p ′ ,∞,loc (Ω) , with α ∈ (0, 1) and p ′ = p/(p − 1). This leads us to obtain higher fractional differentiability results for a function of the spatial gradient Du of the solutions. Moreover, we establish the higher summability of Du with respect to the spatial variable. The main novelty of the above equation is that the structure function satisfies standard ellipticity and growth conditions only outside the unit ball centered at the origin. We would like to point out that the main result of this paper can be considered, on the one hand, as the parabolic counterpart of an elliptic result contained in [1], and on the other hand as the fractional version of some results established in [2].

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