Energy-trapped electromechanical resonators are widely used. A numerical technique for analysis and design, by means of a finite element simulation procedure, is presented in which the electromechanical coupling effect is taken into account. The thickness/shear and the thickness/twist vibrations associated with a piezoelectric thin plate are considered. A circular plate quartz resonator and a plano-bevel DT-cut quartz resonator are analyzed as pseudo-two-dimensional models for test case examples, the results for which are compared with the measured data. The calculation of rectangular plates as two-dimensional examples is then demonstrated, and the effect of the plate width on the natural frequencies is discussed in conjunction with the one-dimensional case. The calculation of the motional admittance at the electrical terminal also is shown.
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