高频纵向导波在钢杆中传播的数值模拟

锚固锚杆中高频导波（大于1 MHz）的低衰减使其具有巨大的潜在应用价值，但高频导波数值计算的复杂性使得确定其传播特征非常困难，只依赖试验确定不同锚固锚杆中的最优激发波并不现实，因此建立高频导波传播的数值模型具有重要意义。应用有限元软件构建钢杆的数值模型，分别研究径向和轴向的单元网格密度和材料阻尼对高频导波传播过程的影响情况，采用所有截面节点幅值叠加和经验模态分解（empirical mode decomposition，简称 EMD 分解）的方法进行数据处理，获得了与文献理论结果及试验测试结果相吻合的高频导波在钢杆中的基本传播特征。研究结果表明，单元网格密度、材料阻尼值设置及不同位置质点的振动叠加是再现高频导波基本传播特征的关键。

Numerical modeling of high frequency longitudinal guided wave propagation in steel rod

The low attenuation of high-frequency guided waves (greater than 1 MHz) in anchoring bolts makes it of great potential application value. However, the complexity of numerical calculation of high-frequency guided waves makes it very difficult to determine its propagation characteristics. It is not realistic to rely only on experiments to determine the optimal excitation wave in different anchorage bolts, so it is of great significance to establish a numerical model of high-frequency guided wave propagation. In this study, we first used the finite element software to construct a numerical model of the steel rod to examine the influence of the radial and axial element mesh density and material damping on the propagation process of high-frequency guided waves. And then, we employed the amplitude superposition and sum of all cross-section nodes as well as empirical mode decomposition (EMD) method to process data. Finally, we obtained the basic propagation characteristics of high-frequency guided waves in steel rods that are consistent with the theoretical results in the literature and experimental test results. The research results show that the element grid density, the setting of material damping value, and the vibration superposition of particles at different positions are the keys to reproducing the basic propagation characteristics of high-frequency guided waves.