Passive Vibration Suppression of Beam with Piezoelectric Elements : An Approach Using Analogies between Electrical and Mechanical Circuits

Abstract

Electrical circuits with piezoelectric elements were used to suppress the vibration of a beam passively. The system was simplified by modeling an electromechanical circuit containing a transformer with a simple equivalent electrical circuit by using a mathematical equation. The effective mechanical impedance for the piezoelectric element shunted by an arbitrary circuit was also expressed in the mathematical equation. It was found that the effective impedance conversion coefficient must be increased in order to use electric elements of conventional size. To increase the conversion coefficient by connecting piezoelectric elements, an arrangement similar to that of a multilayered ceramic capacitor was suggested. As an application, a resistor shunted by the piezoelectric element could increase the loss factor and change the natural frequency of the beam. The added loss factor depends on the device coupling coefficient, while the frequency of the peak of the loss factor curve depends on the resistor. The device coupling coefficient for a large added loss factor was discussed, in contrast to the material coupling coefficient which is usually discussed. Finally, experiments using resistive shunt circuits were conducted to verify simulation results.