Transient responses of a piezoelectric tube scanner

By treating the electric signals applied to a piezoelectric tube scanner for scanning probe microscopy as external excitations, this article gives the exact equations of motion of the scanner. The solution method and process to solve these equations are also presented. The closed form solutions of the equations give the transient responses of the scanner, and show explicitly the extension motion and deflection motion of the scanner subject to a bias. Experiments support the theoretical conclusions. The solutions presented here are useful for the design and analysis of a scanning probe microscope and other systems including piezoelectric tubes as well.