The finite element analysis of the vibration characteristics of piezoelectric discs

Abstract

Finite element methods and modal analysis techniques have been used to predict the vibration characteristics of piezoelectric discs with finite diameter to thickness ( D/T) ratios. The finite element method for piezoelectric materials is formulated in generalized variables and co-ordinates, and the eigenvalue problem is solved directly by treating the electrical term effectively as an extra mechanical degree of freedom. This not only avoids the fully populated stiffness matrix likely to be caused by the condensation technique, but also enables the problem to be solved by a standard finite element package. The mechanical response function for constant voltage excitation and the electrical impedance characteristic functions are also formed. Numerical results are presented for piezoelectric discs with D/T ratios of 20 and 10. Five types of mode are identified according to their mode shape characteristics; these are radial, edge, thickness shear, thickness extensional and high frequency radial modes. However, no mode has been predicted having the piston-like motion assumed in one dimensional theory. The most strongly excited modes of the disc are the thickness extensional modes which are in the frequency range of the first through thickness mode predicted by a one-dimensional model. The finite element results have been checked experimentally, excellent agreement being obtained.