应用兰姆波测定材料弹性参数的反演方法

Inverse Algorithm in Estimation of Elastic Properties of Materials Using Lamb Waves

提出基于兰姆波基础阶对称模式的反演方法来估计材料的弹性常数。兰姆波在存在复杂边界的结构中传播时,时域上边界回波相互混叠,各波包成分难以识别。根据兰姆波的频散特性,选取群速度最快对称模式的低频,用于反演计算。利用相位展开法获取基础阶对称模式的相速度实验值;建立以相速度实验值、弹性常数估计值、频率为变量的误差函数,当误差函数最小时,相速度实验值与基于弹性常数估计值的频散曲线吻合度最好。结合薄铝板、发电机大功率电机的线棒绝缘层、转向架的弹性常数反演过程,并进行误差分析,验证基础阶对称模式反演方法的可行性、通用性。

Based on the basic symmetric mode of Lamb waves, an inverse algorithm is proposed for calculating the elastic properties of different kind of materials. When the Lamb waves propagate in the structure with complicated boundaries, it is difficult to distinguish the components of the waves due to the overlapping of wave reflection on the boundaries. The basic symmetric mode （S0） wave is appropriate for estimating the elastic properties of the materials because of its relatively large group velocity. By using the phase spectrum method, the measured phase velocity can be extracted from the experimental results. An error function depending on the measured phase velocity is introduced. The elastic properties can be inversely determined by minimizing the error function. Finally, the inverse algorithm is tested in estimating the elastic parameters of thin aluminum sheets, rotors and a bogie. The results demonstrate the feasibility and generality of the proposed method.