中文摘要：

提出一种求解波导结构频散特性的有限元特征频率法，该方法基于振动问题的特征频率计算理论，根据模态振型识别波数与模态类型，建立了相速度及群速度的求解方法。该方法可适用于任意波导结构的频散关系求解。首先分析满足收敛精度要求的最大网格单元尺寸与最小模型长度，并用该方法对筒支板条结构的频散特性进行了计算。结果表明，有限元特征频率法适合求解波动频散关系，板条结构中模态受边界影响会产生同阶高次模态，边界尺寸决定新模态的截止频率；随频率的增大，同阶低次反对称模态会趋于一致；对称模态能量分布受边界影响较大。本文也为板条类结构导波实验结果的分析提供了理论依据。

英文摘要：

A new method that finite element eigenfrequency is presented to calculate wave motion prob- lems. This method is based on the solving theory of vibration eigenfrequency, wavenumbers and modes are distinguished by modal shape, and the solution of phase velocity and group velocity are found. This method can be applied to any waveguide structure for the solution of dispersion relations. The maximum mesh element size and the minimum model length were analyzed for the precision requirement. Dispersion relations are calculated in simply supported plate strip. The results show that higher order modes were generated by boundary effect, boundary size decided cut frequency of new modes;with the increase of fre- quency, low order modes were consistent with basis mode;it was obvious that energy distribution affect- ed by boundary in symmetrical modes. This paper also provides a valuable theoretical foundation for the analysis of experimental results.