Optimal configuration and combination of piezoelectric transducer and inductor for synchronized-switch-damping-on-an-inductor technique

Abstract

This article describes the optimal configuration and combination of piezoelectric transducers and inductors for the synchronized-switch-damping-on-an-inductor technique. The technique suppresses structural vibrations by inverting the polarity of the electric voltage in a piezoelectric transducer using a switched inductive shunt circuit at each displacement extremum. The energy dissipation rate of synchronized switch damping on an inductor depends on the impedances of the transducer and the inductor in the circuit, especially the resistive component, in this inversion. For this study, mathematical models of the equivalent resistances of transducers and inductors for this inversion phenomenon were formulated based on experiments with various transducers and inductors. Using these models, the optimal ratio of the thickness–area of patch-type piezoelectric transducers and that of the length–cross-sectional area of the lead of the inductors were analytically obtained. The optimization of series–parallel connections of multiple transducers and inductors was also shown to be equivalent to this one. The optimal mass budget allocation for the transducers and inductors was also formulated. Two examples of optimization, involving an increase in energy dissipation rates by a factor of 4, were presented. The examples showed that the time taken to suppress free vibrations in a clamped beam was reduced to half through the optimization.