Step discontinuities, which are formed in pipeline repair and maintenance, will introduce additional wave scattering in the pipeline diagnosing work. Therefore, an analytical model is established in this paper to investigate the longitudinal wave scattering from a step discontinuity and the influence of discontinuity material on the scattering characteristics in water pipelines. In the model, axial wavenumber, displacement and stress profiles of the unblemished pipeline and discontinuity sections are calculated by a multi-layered cylindrical waveguide model. To concatenate these sections and predict the overall influences of the discontinuity, the mode matching method is applied by enforcing the flexible axial boundary conditions with an extended bi-orthogonality relation. Based on the established model, numerical calculations are carried out to investigate the reflection/transmission characteristics when discontinuity material and attenuation are considered. Both finite element method (FEM) software and laboratory experiments are also conducted for modeling verification: the maximum root mean square errors of the predicted reflection and transmission coefficients are 0.01 and 0.1 compared with FEM and experiment results, respectively. It indicates the proposed model is accurate in predicting the wave scattering from a step discontinuity in a water pipeline with the influence of discontinuity material accounted for. In addition, this pure analytical model introduces advantages in computational cost when modeling long pipelines compared with existing FEM packages.

中文翻译：

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水管道波导中阶梯不连续性的波散射：分析建模和不连续性材料影响

在管道维修和维护中形成的台阶不连续性将在管道诊断工作中引入额外的波散射。因此，本文建立了一个解析模型，研究了台阶间断面的纵波散射以及间断面材料对输水管道中散射特性的影响。在模型中，通过多层圆柱波导模型计算了无缺陷管道和不连续部分的轴向波数、位移和应力分布。为了连接这些部分并预测不连续性的整体影响，通过使用扩展的双正交关系强制灵活的轴向边界条件来应用模式匹配方法。基于已建立的模型，当考虑不连续材料和衰减时，进行数值计算以研究反射/透射特性。还进行了有限元法（FEM）软件和实验室实验进行建模验证：与FEM和实验结果相比，预测反射和透射系数的最大均方根误差分别为0.01和0.1。这表明所提出的模型在预测水管道中台阶间断的波散射方面是准确的，其中考虑了间断材料的影响。此外，与现有 FEM 包相比，这种纯分析模型在对长管道进行建模时在计算成本方面具有优势。