Optimization of piezoelectric patch positioning for passive sound radiation control of plates

The purpose of this article is the optimization of piezoelectric patch positioning for reducing the radiated sound power of thin plates. To this end, an aluminium plate equipped with a set of piezoelectric patches connected to a passive circuit is considered. The difficulties in designing a smart structure are not only related to the conception of the electric circuit used as controller, but also to the choice of how the circuit itself is coupled with the structure. The selection of the number of transducers to be used, and their positioning, is a crucial step in the designing process. In this work the entire design process of a smart structure is proposed, with the goal of obtaining the best efficiency in terms of reduction of radiated sound power, while using a lightweight optimization procedure in terms of computational costs. To this end, classical instruments of vibrations mechanics are used together with acoustic concepts, such as the modal radiation efficiency. The introduction of this acoustic characterization of the structure in the optimization process is done by using a new utility function, the acoustic controllability, which will be used for the optimization of transducer positioning. The proposed optimization process is applied to the case study of an aluminium plate with nonstandard boundary conditions, and experimental results confirm the validity of this novel procedure.