Piezoelectric passive distributed controllers for beam flexural vibrations

Recent technological developments have made available efficient bender transducers based on the piezoelectric effect. In this paper an electrical circuit analog to the Timoshenko beam is synthesized using a Lagrangian method and by paralleling capacitive flux linkages to rotation and transverse displacement. A Piezo-ElectroMechanical (PEM) beam is conceived by uniformly distributing piezoelectric transducers on a beam and interconnecting their electric terminals via the found analog circuit, completed with suitable resistors. The high performance features of the synthesized novel circuit include the following. (i) The circuit topology is extremely reduced, the used components are all but one two - terminal elements, and the only two port network needed is an ideal transformer, (ii) One and the same dissipative circuit ensures a multiresonance coupling with the vibrating beam and the optimal electrical dissipation of mechanical vibrations energy, (iii) For a prototype of a PEM beam, the design of the analog circuit is possible and the obtained nominal values of the circuital elements ensure that can be technically realized without any external feeding. The insertion of resistors in the analog circuit is determined according to two optimality criteria (namely minimization of strain energy time envelope and maximization of vibration time rate decay), based on specific engineering needs. The former seems to be suitable for applications in fatigue phenomena and the latter when the amplitude of vibrations must be rapidly decreased, independently of the initial conditions.