Analysis of Natural Vibrations of Round Flexing Membrane-Type Piezoelectric Transducers with an Arbitrary Dimension Ratio

The problem of natural vibrations of a round exing membrane-type piezoelectric transducer (piezoelectric plate) with an arbitrary dimension ratio is solved in the exact formulation using the finite element method for two variants of fastening the membrane (simply supported and rigidly fixed plate). The natural frequency spectra are analyzed in the resonance and antiresonance regimes. The displacement distributions over the plate surfaces are also analyzed and the dependences of the dynamic electromechanical coupling coefficient are investigated as functions of the geometric dimensions of the piezoelectric transducer, the plate material, and the piezoelectric ceramic composition. The optimum geometric dimensions of the transducer which ensure the maximum dynamic electromechanical coupling coefficient are determined and the value of the coefficient is estimated.