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A method for the analysis of piezoelectric media based on finite-element calculations is presented in which the fundamental electroelastic equations governing piezoelectric media are solved numerically. The results obtained by this finite-element calculation scheme agree with theoretical and experimental data given in the literature. The method is applied to the vibrational analysis of piezoelectric sensors and actuators with arbitrary structure. Natural frequencies with related eigenmodes of those devices as well as their responses to various time-dependent mechanical or electrical excitations are computed. The theoretically calculated mode shapes of piezoelectric transducers and their electrical impedances agree quantitatively with interferometric and electric measurements. The simulations are used to optimize piezoelectric devices such as ultrasonic transducers for medical imaging. The method also provides deeper insight into the physical mechanisms of acoustic wave propagation in piezoelectric media.
Reinhard Lerch (Tue,) studied this question.