Multimodal Vibration Damping through Piezoelectric Patches and Optimal Resonant Shunt Circuits

Piezoelectric elements connected to shunt circuits and bonded to a mechanical structure form a dissipation device that can be designed to add damping to the mechanical system. Due to the piezoelectric effect, part of the vibration energy is transformed into electrical energy that can be conveniently dissipated. Therefore, by using appropriate electrical circuits, it is possible to dissipate strain energy and, as a consequence, vibration is suppressed through the added passive damping. From the electrical point of view, the piezoelectric element behaves like a capacitor in series with a controlled voltage source and the shunt circuit, commonly formed by an RL network, is tuned to dissipate the electrical energy, more efficiently in a given frequency band. It is important to know that large inductances are frequently required, leading to the necessity of using synthetic inductors (obtained from operational amplifiers). From the mechanical point of view, the vibration energy can be attenuated in a single mode, or in multiple modes, according to the design of the damping device and the frequency band of interest. This work is devoted to the study of passive damping systems for single modes or multiple modes, based on piezoelectric patches and resonant shunt circuits. The present contribution discusses the modeling of piezoelectric patches coupled to shunt circuits, where the basics of resonant shunt circuits (series and parallel topologies) are presented. Following, the devices used in passive control (piezoelectric patch and synthetic inductors) are analyzed from the electrical and experimental viewpoints. The modeling of multi-degree-of-freedom mechanical systems, including the effects of the passive damping devices is revisited, and, then a design methodology for the multi-modal case is defined. Also, it is briefly reviewed the optimization method used for design purposes, namely the LifeCycle Model. Finally, experimental results are reported, illustrating the success of using the methodology presented in passive damping applications applied to mechanical and mechatronic systems.