A 2-D semianalytical model using the Legendre polynomial approach was applied for modeling the piezoelectric transformer (PT). In the model, the mechanical displacements and the electric potential were expanded in a double series of orthonormal polynomials with an appropriate analytical form. Series and parallel resonance frequencies, input electrical admittance, and voltage gain were obtained for the PT. The results are in excellent agreement with both the numerical results calculated with a 3-D finite-element analysis and experimental ones. The approach is able to predict the behavior of a wide and a long PT.

中文翻译：

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利用多项式方法对Rosen型压电变压器进行二维建模。

将使用勒让德多项式方法的二维半解析模型应用于压电变压器（PT）的建模。在模型中，将机械位移和电势扩展为具有适当解析形式的双正交正交多项式序列。获得了PT的串联和并联谐振频率，输入电导率和电压增益。结果与通过3-D有限元分析计算出的数值结果和实验结果均非常吻合。该方法能够预测宽和长PT的行为。