Modeling of conventionnal piezoelectric resonators by Hamilton's principle using mode acceleration method

This article deals with an energetic approach to model the electromechanical behaviour of conventional piezoelectric resonators composed of PZT-type ceramics. The semi-analytical model developed in this paper is based on a... [ view full abstract ]

This article deals with an energetic approach to model the electromechanical behaviour of conventional piezoelectric resonators composed of PZT-type ceramics. The semi-analytical model developed in this paper is based on a variational approach, to wit Hamilton's principle, and illustrated on a geometry using the transverse piezoelectric coupling.

Mechanical and electrical equations are deduced and solved by using the mode expansion method. As a consequence, the main features and performance assessment of the first symmetric longitudinal vibrations modes can be studied as well as the frequency response of electrical quantities. In concrete terms, methodology is detailed and measurable mechanical and electrical quantities are computed, especially the frequency response of the longitudinal component of the displacement field and input admittance.

Furthermore, the mode acceleration method is presented to improve the mechanical mode computation. The objective of this method is to replace the high-frequency vibration modes in the mode expansion of the solution with their static contribution. This "quasi-static correction" gives rise to a much richer model than the one using only the modal expansion for a same number of mechanical degrees of freedom to calculate. This approximation just needs an extra computation in order to determine the quasi-static longitudinal component of the displacement field by solving a system of linear equations. Results are compared with numerical and experimental data for discussion and validation.

Finally, even if the example concerned is common and well-known, the method deployed will be able to be advantageously applied to more complex geometries like piezoelectric transformers.