中文摘要：

为了获得各向同性均质自由铝板中兰姆波的频散特性曲线，采用了半解析有限元方法。此方法仅需要在自由板的横截面进行有限元离散，而假定兰姆波沿波的传播方向以简谐振动的方式运动，由哈密顿原理推导出兰姆波在自由板中传播的波动方程，通过特征方程求解得到波数和频率的关系。通过半解析有限元方法可以绘制各向同性均质自由铝板中兰姆波的相速度频散曲线，不需模态跟踪，由特征值和特征向量可直接求解得到群速度频散曲线，由特征向量可进行兰姆波的振动模态分析，这种方法还可推广用于任意横截面形状波导介质中导波模态的求解。

英文摘要：

The semi-analytical finite element （SAFE） method is used to obtain Lamb wave dispersion curves in an isotropic homogeneous free aluminum plate. This approach only requires the finite element discretization on the cross- section of the plate, and assumes that Lamb wave is a harmonic motion along the wave propagation direction. The Hamilton＇s principle is used to obtain the wave equation with which the Lamb wave propagates in the free plate; and the relationship between wavenumber and frequency is obtained by solving a twin-parameter generalized eigenproblem. The SAFE method is used to plot the dispersion curve of Lamb wave phase velocity in an isotropic homogeneous free aluminum plate. The eigenvectors obtained with SAFE method reflect the vibration modes of the Lamb waves in the plate, and the eigenvalues and eigenvectors can be used to obtain the dispersion curve of the group velocity directly. The SAFE method can also be used to acquire dispersion curves for waveguides with arbitrary cross-section.