| In this thesis three kinds of piezoelectric transformers are investigated, including circular cylinder piezoelectric transformer of thickness-shear mode, cylindrical thin shell piezoelectric transformer of torsional mode and multi-layered rectangular plate piezoelectric transformer of thickness-twist mode. The weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance is also analyzed.Chapter one is contributed to reviewing preceding research on piezoelectric transformer in details, introducing history and development of this field and classifying the final research conclusion. Finally the investigate methods in this dissertation are introduced.Chapter two presents the three-dimensional equations of the nonlinear theory of electroelasticty for large deformations and strong fields and the linear theory of piezoelectricity for infinitesimal deformation and fields.Chapter three and four analyze two kinds of piezoelectric transformers based on the three-dimensional piezoelectric linear theory and methods of thickness-shear mode circular cylinder piezoelectric transformer and torsional mode cylindrical thin shell piezoelectric transformer. Finally output voltage, input admittance, and efficiency of the transformer are discussed on the basis of numerical calculations.Chapter five investigates thickness-twist vibration of a multi-layered rectangular piezoelectric plate of crystals with 6mm symmetry or polarized ceramics. An exact solution is obtained from the three-dimensional equations of linear piezoelectricity, which set a piezoelectric transformer as an example to analyze.Chapter six analyzes the nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution is obtained. It also presents numerical results based on the analytical solution.Chapter seven summarizes the paper and concludes some useful points. Further investigations on this problem are prospected. |
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