Optimal Piezoelectric Potential Distribution for Controlling Multimode Vibrations

Vibration damping is prominent in engineering; in fact, vibrations are related to many phenomena (e.g., the fatigue of structural elements). The advent of smart materials has significantly increased the number of available solutions in this field. Among smart materials, piezoelectric materials are most promising. However, their efficiency depends on their placement. There are many studies on their optimal placement for damping a particular mode, but few account for multimodal vibrations damping. In a previous work, an analytical method was proposed to find the optimal placement of piezoelectric plates to control the multimode vibrations of a cantilever beam. In this study, the efficiency of the above method has been improved, considering all plates active simultaneously, regardless of the eigenmodes that are excited, and changing, instead of the plates, the potential distribution. The method results indicate the optimal potential distribution for different excited eigenmodes. The results have been compared with those obtained by experimental tests and numerical simulations, exhibiting very good agreement.