Multimodal vibration control by using piezoelectric transducers and passive circuits

In this paper we solve the problem of finding an optimal passive electrical controller of beam vibrations exploiting distributed piezoelectric transducers. To this aim an electrical circuit analog to a Euler beam is synthesized using a Lagrangian method and by paralleling capacitive flux linkages to rotations and transverse displacements. Therefore a piezo-electromechanical (PEM) beam is conceived by uniformly distributing piezoelectric transducers on a beam and interconnecting their electrical terminals via the found analog circuit, completed with suitable resistors. The high-performance features of the synthesized novel circuit include: i) the circuit topology is extremely reduced, the used components are all but one two-terminal passive elements, and the' only two-port network needed is an ideal transformer; ii) one and the same dissipative circuit assures a multi-resonance coupling with the vibrating beam and the optimal electrical dissipation of mechanical vibration energy.