A model for the theoretical characterization of thin piezoceramicrings

摘要

This work describes a matrix model of the radial mode of a thinnpiezoceramic ring capable of predicting the dynamic behavior when thentwo main surfaces are stress free, while the lateral, inner, and outernare loaded by an external medium. The ring is modeled as a three-portnsystem with two mechanical ports and one electrical port. With thisnapproach it is easy to compute the resonance frequency spectrum, thenradial displacement, and the electric impedance of a thin ring. Goodnagreement between the computed and the measured electric impedance isnfound. The resonance frequency spectrum is computed as a function of theninner-to-outer radius ratio G: when the inner radius vanishes, thenresonances of the ring coincide with those of a disk, while, increasingnG up to one, the first-mode frequencies decrease approaching the valuenobtained with a lumped mode model. The frequencies of the higher-ordernmodes, on the other hand, increase to infinity, justifying the lumpednmode approximation. The spatial distribution of the displacement in thenradial direction is also computed; it has a Bessel function shape which,nas expected, becomes linear by increasing the inner radius. Finally, thenbehavior of the effective coupling factor keff with G isnexamined. It is shown that, when G→1, keff approachesnthe material coupling factor k31, while when G→0,nkeff is proportional to the planar coupling factor kpn. Further it is shown that for G>0.6, the approximation of thenring to a lumped mode system is quite acceptable