Analysis of the radial symmetrical modes of thin piezoceramic rings

In this work, the radial symmetric vibration modes of thin piezoceramic rin gs have been analysed by means of a previously proposed theoretical model. Both the resonance frequencies and the effective electromechanical coupling factor (k(eff)), as a function of the aspect ratio G between the inner and outer radii of the ring, were computed. The results have shown that the di sk structure (G --> 0) has only one radial symmetrical mode (with its harmo nics), but, for the ring structure (G --> 1), two different modes are clear ly distinguished: the ring mode, which has no harmonics, and a width-like m ode, with its harmonics. Moreover, the results show that the ring structure can be assumed to be definitely reached for G > 0.6. An analysis of the ma terial coupling factor in the ring geometry is reported as well.