An analysis of space-dependent electric fields used in exciting flexural vibrations of piezoelectric beams

Abstract

Expressions for the mechanical deflection and the piezoelectric current of a piezoelectric beam located in a general electric field are derived. It is shown that the relationships between the interesting macroscopic electric and mechanical quantities are determined by only three integrals. Two of these are proportional to each other for a beam and the third is normally negligible. The remaining integral depends only on the dielectric field and can be determined by using the well known Laplace equation. The value of this integral can be estimated accurately without the need of a computer. It is shown by eigenmode decomposition that it is enough to study the static case in order to find the dynamic behaviour. The integrals are used in order to study some electrode configurations. It is indicated how the most efficient electrode configuration, for a given direction of vibration, can be determined.