Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners

Flexural resonance vibrations of piezoelectric ceramic tubes in Besocke-style scanners with the nanometer resolution are studied by an electro-mechanical coupling Timoshenko beam model. Meanwhile, the effects of frictions, the first moment and moment of inertia induced by mass loads are considered. The predicted resonance frequencies of the ceramic tubes are sensitive to not only the mechanical parameters of the scanners, but also the frictions acting on the attached shaking ball and corresponding bending moment on the tubes. The theoretical results are in excellent agreement with the related experimental measurements. This model and corresponding results are applicable for optimizing the structures and performances of the scanners.