11. Multimodal Damping of a Plate with a Passive Piezoelectric Network

Multimodal vibration reduction can be obtained by coupling a mechanical structure to an electrical network approximating its modal properties. This strategy is applied to the control of a clamped plate with a 2D network of passive electrical components. The plate and the network are coupled through a periodic array of piezoelectric patches that enables the energy conversion. The network is experimentally implemented with inductors and transformers in order to create electrical resonances that present a spatial distribution approaching the first mode shapes of the plate. By tuning electrical resonances to mechanical ones, it becomes possible to introduce the equivalent of a tuned mass effect. This effect only occurs if the electrical and mechanical mode shapes are sufficiently close, which requires specific network topology and boundary conditions. Once the network is tuned, adding resistors introduces damping that can lead to a broadband vibration reduction of the plate. It is thus shown that a 2D control can be implemented with a purely passive solution, which could be of great interest for many embedded applications.