Measurement and prediction of the frequency spectrum of piezoelectric disks by modal analysis

The dependence of the vibration characteristics of a piezoelectric disk on its geometry, particularly the diameter to thickness ratio (D/T ratio), is studied by a finite element model and modal analysis. The frequency spectrum that correlates the vibration characteristics (product of resonance frequency and the thickness of the disk, fT) with the geometrical properties of the piezoelectric disk (D/T ratio) is predicted by the finite element model in the D/T ratio range from 0.1 to 20. The modal constant at each resonance is calculated using modal analysis techniques to obtain the strength of each resonance in the frequency spectrum when the disk is excited by a voltage applied to electrodes on its top and bottom surfaces. It is shown that the thickness extensional modes have much larger modal constants than the other modes in the spectrum especially in disks with D/T ratios larger than 5, and as the D/T ratio of the disks increases the number of the thickness extensional modes increases, while the response is gradually dominated by fewer and fewer modes, and finally by a single mode. The predictions have also been checked by experiment and in general good agreement has been obtained between the experiments and the predictions. The results indicate that the modal constant approach is a convenient and reliable means of assessing the strength of excitation of a given mode both numerically and experimentally.