A gradientless technique for optimal distribution of piezoelectric material for structural control

Application of smart piezoelectric materials in structural control is gaining momentum. Optimum placement and actuation of the smart material is an aspect of paramount importance in such structures. In this paper, we present an iterative technique to optimize the shape of piezoelectric actuators in order to achieve the desired shape of the structure. A C0-continuous eight-node plate nite element with ve degrees of freedom is employed. A gradientless shape design procedure based on the residual voltages is developed. It aims at minimizing the quadratic measure of the global displacement residual error between the desired and the current structural con guration. The actuators gradually adapt to a shape that is most e cient in resisting the external excitation. The present technique can be well suited for any static and time-varying excitation. In vibration control it is often necessary to create modal sensors and actuators in order to observe or excite some speci c modes. Such modal sensors and actuators alleviate spillover problems and thus they avoid exhaustive signal processing. Several numerical examples for static as well as dynamic cases are presented to demonstrate the e cacy of the present technique