A matrix model of the thin piezoceramic ring

In this work we describe a matrix model of the thin piezoceramic ring which, taking the interaction with the surrounding media into account, is able to compute all the ring transfer functions. A good agreement between computed and measured electric input impedance was found. The resonance frequency spectrum, as a function of the inner to outer radius ratio G, was computed: when the inner radius vanishes, the resonances of the ring coincide with those of a disk, while, increasing G up to one, the first mode frequencies decrease approaching the value obtained with the lumped mode model. Finally, the model makes it possible to compute the spatial distribution of the displacement in the radial direction; it has a Bessel function shape which, as expected, becomes linear increasing the inner radius