Flexural vibration analyses of piezoelectric ceramic tubes with mass loads in ultrasonic actuators.

Based on Timoshenko beam model, a theoretical model of radially polarized piezoelectric ceramic tubes is investigated. In the model, the piezoelectric effects are considered, and the shear correction factor is introduced which reveals effects of the size of the cross-section and Poisson's ratio. Based on the model, the particular attentions are devoted to effects of the boundary conditions at two ends on flexural resonance frequencies of the piezoelectric ceramic tubes. Changing the sizes of the tubes and the mass loads at both free ends, the variations of the flexural resonance frequencies of free-free piezoelectric ceramic tubes are calculated theoretically. Besides, the flexural resonance frequencies of the piezoelectric ceramic tube cantilevers with mass loads at one free end are also investigated theoretically. To verify accuracy of the theoretical mode, the flexural resonance frequencies for different lengths of the piezoelectric ceramic tubes and different loaded masses are measured experimentally. The theoretical results agree well with the experimental measurement, which demonstrates that the model is accurate for analyzing the flexural resonance frequencies of the piezoelectric ceramic tubes with mass loads.