A phenomenological method of predicting the performance of piezoelectric beams

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Abstract
A simple and phenomenological method for the prediction of the performance of piezoelectric beams is studied. It is shown that strong resemblance between flexural, longitudinal and torsional vibrations exists in the piezoelectric case. The important information can, for all three types of vibration, be assembled in three integrals. One of these is normally negligible and the other two are related to each other. One can therefore choose to treat the beam as purely piezoelectric (Poisson's equation) or purely dielectric (Laplace's equation). The piezoelectric behavior, including the values of the well-known piezoelectric equivalent components, can be predicted once the values of the integrals are known. These values can be found using simple mathematical tools.

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