A mathematical analysis of a smart-beam which is equipped with piezoelectric actuators

First of all, a brief reminder on piezoelectric effect is given. Then it is applied to a beam equipped with such actuators. The influence of tile shape and location is discussed. A smart beam model is finally presented and analyzed. The controllability is carefully examined in the framework of the H.U.M. method of Lions (1988). Let us also underline that the asymptotic harmonic behaviour of the structure is videly used.