Passive multi-mode piezoelectric shunt damping: an approach based on matrix inequalities

Piezoelectric shunt damping is a well-known technique for suppressing vibrations in light mechanical systems. The method is based on the connection of a properly designed electrical network (shunt circuit) to a piezoelectric actuator bonded to the vibrating structure. This network can be either passive (i.e. made from resistances, capacitances and inductances) or active. When active shunts are used, possible problems related to instability of the system can raise. This paper addresses a new approach for designing shunt electrical circuits allowing to damp more than one mechanical mode of the structure at the same time with a single piezoelectric actuator. Moreover, the method assures to design passive shunt impedances, thus avoiding instability problems. Starting from a state space description of the electro-mechanical system, the definition of the shunt circuit is achieved using an approach based on matrix inequalities, which allows to design shunt circuits with different goals by expressing the desired target as a single or a system of matrix inequalities.