Piezoelectric sensor and actuator spatial design for shape control of piezolaminated plates

Controlled actuation and sensing of structures by spatially distributing the piezoelectric material has been a topic of interest in recent years. We present an iterative technique to design the shape of piezoelectric actuators in order to achieve the desired shape of the structure. A gradientless shape design procedure based on the residual voltages is developed. It aims at minimizing the quadratic measure of global displacement residual error between the desired and the current structural configuration. The actuators gradually adapt to a shape that is most efficient in resisting the external excitation. The present technique can be well suited for an 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 specific modes. Such modal sensors and actuators alleviate spillover problems, and thus they avoid exhaustive signal processing. Several numerical examples for static as ell as dynamic cases are presented to demonstrate the efficacy of the present technique