基于Bloch-Floquent理论和有限元仿真的板结构Lamb波复频散关系研究

Study of Lamb-Wave Complex Dispersion Relations for Plate Structures Based on Bloch-Floquent Theory and Finite Element Simulation

针对板结构中Lamb波频散和多模态限制其在超声无损检测技术中实际应用的问题,文中使用了一种基于Bloch-Floquent理论和有限元特征频率法的方法,计算得到了钢板结构在实数波数域和纯虚数波数域包含模态信息的频散曲线。利用Bloch-Floquent周期性边界条件对板结构进行了较大简化,快速计算了无限大钢板结构在不可约布里渊区和纯虚数波数域内的频散曲线。通过Bloch-Floquent扩展和傅里叶变换准确获得了各特征模式的真实波数信息,克服了频散曲线混叠的问题。根据各个模式上下表面的离面位移进行了模态识别,从而得到了钢板完整的频散关系。该方法的计算结果与通过传统二分法求解频散方程所得到的结果具有较大一致性,验证了该方法的有效性。

In order to solve the problem of Lamb wave dispersion and multi-mode restriction in plate structure and its practical application in ultrasonic nondestructive testing technology,a method based on Bloch-Floquent theory and finite element characteristic frequency method is used to calculate the dispersion curve of plate structure containing mode information in real and pure imaginary wave number domains.Based on the Bloch-Floquent periodic boundary conditions,the dispersion curves of infinite steel plate structures in irreducible Brillouin region and pure imaginary wave number domain are quickly calculated.In this study,Bloch-Floquent extension and Fourier transform are used to obtain the real wave number information of each characteristic mode and overcome the aliasing problem of dispersion curve.In this study,the modal identification is carried out according to the out-of-plane displacements of the upper and lower surfaces of each mode,and the complete dispersion relation of the steel plate is obtained.The calculated results of this method are in good agreement with those obtained by solving the dispersion equation with the traditional dichotomy method,which verifies the validity of this method.