Dynamics of piezoelectric tube scanners for scanning probe microscopy

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Abstract
This article considers the equations of motion of piezoelectric tubes used as transducers in scanning tunneling microscopy and other scanning probe microscopies. Solutions for the dynamics responses of the tube are obtained for both extension and bending. The lowest frequency resonances are found for some common designs of tube scanner, and the results compared with available experimental data. It is shown that the response is determined by the load carried by the tube, as well as by its material properties and geometry.