A model for the theoretical characterization of thin piezoceramic rings

This work describes a matrix model of the radial mode of a thin piezoceramic ring capable of predicting the dynamic behavior when the two main surfaces are stress free, while the lateral, inner, and outer are loaded by an external medium. The ring is modeled as a three-port system with two mechanical ports and one electrical port. With this approach it is easy to compute the resonance frequency spectrum, the radial displacement, and the electric impedance of a thin ring. Good agreement between the computed and the measured electric impedance is found. The resonance frequency spectrum is computed as a function of the inner-to-outer radius ratio G: 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 a lumped mode model. The frequencies of the higher-order modes, on the other hand, increase to infinity, justifying the lumped mode approximation. The spatial distribution of the displacement in the radial direction is also computed; it has a Bessel function shape which, as expected, becomes linear by increasing the inner radius. Finally, the behavior of the effective coupling factor k(eff) with G is examined. It is shown that, when G --> 1, k(eff) approaches the material coupling factor k(31), while when G --> 0, k(eff) is proportional to the planar coupling factor k(p). Further it is shown that for G > 0.6, the approximation of the ring to a lumped mode system is quite acceptable.