Analytical modeling of piezoelectric ceramic transducers based on coupled vibration analysis

Abstract

The energy method for analyzing piezoelelctric ceramic transducers [B. S. Aronov, JASA, 117(1), 210‐220.] is applied to the treatment of transducers with mechanical systems that can be cobsidered as two‐dimensional. Analysis is made following the general outline of the theory of coupled vibration in two degree‐of‐freedom systems and its extention to calculating the resonance frequencies of elastic bodies, as suggested by Gibbe and Blechshmidt [Ann. Physik, Ser. 5, 18, No. 5, 417‐485 (1933)]. The approach to the problem is illustrated with examples of piezoelectric rectangular plates, stripes and thin‐walled cylinders at various orientations relative to crystallographic coordinate system. For all of the examples the resonance frquencies and effective coupling coefficients are presented as functions of the dimensional aspect ratios. Equivalent electromechanical circuits are introduced that permit calculation of the transducers performance under different loading conditions. Practical recommendations for improving the electromechanical properties of the transducers by use of appropriate aspect ratios are discussed.