Bandgap control with local and interconnected LC piezoelectric shunts

This paper reports on the control of longitudinal wave propagation, in the kHz frequency range, using local and interconnected LC (inductance-capacitance) shunts distributed periodically along a rod. The LC shunts are connected to piezoelectric inserts and tuned to engender narrow or broad-band pass-bands in the forbidden band frequency range. The Bragg-scattering bandgaps are the result of the periodic mechanical mismatch between PMMA (polymethyl-methacrylate) of the rod and PZT (lead-zirconate-titanate). The narrow pass-bands correspond to the local configuration, where an equivalence between the mechanical impedance of the PMMA and PZT occurs around the shunt resonance frequency. Conversely, the interconnected shunts give a way to an electrical medium through which energy can propagate parallel to its mechanical counterpart, leading to broad pass-bands. This paper presents analytical models for calculating the dispersion and displacements of the 1D medium with interconnected LC shunts. An analytical formulation is also introduced to expediently identify the location of bandgaps and pass-bands in the medium comprised of local LC shunts. Moreover, analytical investigations are carried out to elucidate different physical phenomena giving rise to these pass-bands. The findings are experimentally validated using a finite periodic rod. The ability to tune the dispersion properties of the medium to control the width or depth of the bandgap, by utilizing local or interconnected shunts, offers a new and powerful application for piezoelectric shunts.