Asymptotic analysis of radial vibration of thin piezoelectric disks

Abstract

AbstractThe one‐dimensional radial vibration model of piezoelectric disks has been widely used to determine the relevant material coefficients from admittance measurements. However, the one‐dimensional model assumes infinitely thin disks, and therefore cannot predict their axial displacements. We extend the one‐dimensional model by performing an asymptotic analysis of the axisymmetric radial vibration of thin disks. The asymptotic expansions include the asymptotic axial displacement and the second‐order corrections to the admittance and the radial displacement in the one‐dimensional model. We verify the asymptotic expansions and the one‐dimensional model with the Chebyshev tau method. In the one‐dimensional model, the frequencies of the maximum admittance in the first and second radial modes are accurate to 1% for Pz27 disks with thickness‐to‐diameter ratios of 0.15 and 0.065, respectively. For a general piezoelectric disk in the forced vibration, the error of in the one‐dimensional model can be estimated from the second‐order correction of the asymptotic resonance frequency in the free vibration.