Analysis of the mechanically-uncoupled electric resonance in tapered-thickness piezoelectric transducers

A staircase model of tapered piezoelectrics is used to show that contrary to the case of conventional transducers, which are either mass-controlled below resonance or stiffness-controlled above resonance, thickness tapering produces periodically alternating regions of mass control and stiffness control along the length of a device. Interaction between these mass and stiffness regions contributes to a resonance peak in the electric input impedance, which is shown not to be coupled to the distributed half-wavelength resonances of the device. The theoretical pulse response obtained with the model is shown to be in close agreement with the measured wideband, uniform amplitude pressure profile of a tapered piezoelectric transducer