Lamb wave has been widely used as a non-destructive testing tool for inspecting the defects or damage in the plate system. A comprehensive understanding and correct prediction of the modal characteristics of Lamb waves are of high importance for ensuring successful practical applications. In this paper, a new method called the semi-analytical peridynamic (SAPD) method for analyzing wave propagation is developed. This method, within the framework of the general acoustoelasticity theory, uses the peridynamic differential operator to transform the equations of motion for guided waves in prestressed anisotropic media and the boundary conditions from local differential forms to nonlocal integral forms. By introducing meshfree discretization and Lagrange multipliers, these governing equations can be reorganized into a standard generalized eigenvalue formalism and solved. The effectiveness and accuracy of the SAPD method are first verified through comparison with the exact solutions. Phase and group velocity dispersion curves and displacement distributions of Lamb waves in three typical cases are then calculated to study the effects of material heterogeneity, applied stress and residual stress on the propagation of Lamb waves. Since complex grid generation algorithms are avoided, the SAPD method exhibits the advantages in terms of simplicity and implementation.

中文翻译：

---

用于声弹性 Lamb 波模态分析的半解析近场动力学方法


兰姆波已被广泛用作检测印版系统中缺陷或损坏的无损检测工具。全面理解和正确预测兰姆波的模态特性对于确保成功的实际应用非常重要。在本文中，开发了一种称为半解析近场动力学 （SAPD） 方法的新方法，用于分析波的传播。该方法在一般声弹性理论的框架内，使用近动力微分算子将预应力各向异性介质中导波的运动方程和边界条件从局部微分形式转换为非局部积分形式。通过引入无网格离散化和拉格朗日乘子，这些控制方程可以重组为标准的广义特征值形式并求解。首先通过与确切解决方案的比较来验证 SAPD 方法的有效性和准确性。然后计算三种典型情况下 Lamb 波的相群速度色散曲线和位移分布，以研究材料异质性、外加应力和残余应力对 Lamb 波传播的影响。由于避免了复杂的网格生成算法，因此 SAPD 方法在简单性和实现方面表现出优势。