Analysis of natural vibrations of round bimorph piezoelectric ceramic plates of arbitrary dimensions. II. Rigidly fixed piezoelectric plate

The problem of natural vibrations of a round bimorph rigidly fixed supported piezoelectric ceramic plate (piezoplate) of an arbitrary thickness with arbitrary axisymmetric electrodes is solved using the method of finite elements. The natural frequency spectra are analyzed in the resonance and antiresonance regimes. The displacement distributions over the piezoplate surfaces (vibration modes) are also analyzed and the dynamic electromechanical coupling coefficient (DCC) is investigated as a function of the relative plate thickness for various piezoelectric ceramic compositions. Round bimorph piezoplates with partial electrodes are considered; it is shown that the DCC can be significantly (by tens times) raised using partial electrodes. The results obtained make it possible to estimate the limits of applicability of the approximate one-dimensional theory and choose the optimum geometric dimensions of the plate and electrodes that ensure the maximum DCC.