Prediction of the resonant frequency of piezoelectric tube scanners through three-dimensional finite element modeling of a tube assembly

In this paper, we study the resonant behavior of a piezoelectric tube scanner used in scanning probe microscopes. In particular, we use a finite element model to allow the inclusion of boundary effects, i.e., nonrigid bonding layers and elastic tip holder, on the dynamic response of the scanner. We show that although existing analytical models provide a good estimation of the axial resonant frequency, their predictions of the first bending resonance may have up to a 100% error. In addition, a simple procedure is proposed that combines some precalculated factors to predict the lowest resonant frequency for a wide range of typical scanner dimensions. An experiment is carried out to illustrate the procedure and validate the prediction.