Passive damping of several resonances using multi-branch resonant piezoelectric shunts

Vibration damping using resonant piezoelectric shunts is a method to reduce the amplitude of mechanical resonances by coupling an electrical circuit to a structure through a piezoelectric transducer. The shunt consists of an inductor which creates a resonator tuned to the frequency of the mode to be controlled. In order to damp several resonances simultaneously, multi-branch shunts can be used. Multiple electrical lines are then connected to a single piezoelectric patch. In this work, focused on purely passive control, a circuit involving resistors in series with the inductors is considered. Indeed, each wire wound inductor is usually associated with a non-negligible series resistance due to copper losses. Several multi-branch shunt architectures have been proposed in the literature. From a selection based on their feasibility in passive control, two solutions are retained: the Hollkamp shunt and the current blocking shunt. After numerical implementation, the two architectures are compared, notably by evaluating the effect of the inductance variations with respect to their nominal values and highlighting the influence of additional resistors.