Piezoelectric cylindrical discs and solid rods: Dependence of the resonance frequencies and effective coupling coefficients on aspect ratio.

Dependencies of the resonance frequencies and effective coupling coefficients for solid circular cylindrical piezoelements (discs) of finite size are considered as a function of their height-to-diameter aspect ratios, h/2a. At aspect ratios in the range of approximately 0.5 < h/2a < 1.5 the piezoelements are treated analytically, as a two degree-of-freedom coupled system by applying the coupled mode theory approach [Aronov, Bachand, and Brown, J. Acoust. Soc. Am. 126(6), 2983-2990 (2009)]. Results are presented as plots of resonance frequencies and effective coupling coefficients vs aspect ratios. Experimental verification showed good agreement with the analytical predictions and allowed sufficiently reliable characterization of the trends of parameters in the range of aspect ratios, for which the analytical treatment could not be applied. The equivalent parameters that characterize energy relations in the course of coupled vibration are determined, and the equivalent electromechanical circuit is introduced for calculating frequency response of the transducers.