Abstract:
Thermal behavior is successfully included in a model for the piezoelectric thickness vibrator. The process of building this complete model consists of four steps. The first step is thermodynamic consideration of material properties. Second, the governing partial differential equations, including thermodynamics, are derived for the general case of a piezoelectric material and applied to the specific case of a thickness vibrator. The third and fourth steps are a bond graph analysis of the thickness vibrator, under conditions of heat conduction only, and for the full electro--mechano--thermal interactions. Among the proposed two simple material property models, the isentropically linear and isothermally linear models, the former is selected for the bond graph model as it makes the analysis easier and can be shown to produce very little difference from the isothermally linear assumption. In order to evaluate the usefulness of the developed modeling method for design of transducers, the calculation results for a simple case are compared with the results from experiments. In general, the predictions and the experimental data agree well.