In this paper, a numerical method is proposed to investigate the propagation of elastic guided waves in the armors protecting cylindrical structures, such as cables and pipes, and evaluate the feasibility of using these waves in the context of non-destructive evaluation and structural health monitoring. Armors usually consist of a large number of helical wires in contact with polymeric sheaths surrounding the structure. The numerical method combines a semi-analytical finite element method written in twisting coordinates, which accounts for the continuous screw symmetry of the problem along the structure axis, with rotational Bloch conditions in the cross-section in order to account for the high order of the discrete circular symmetry. The proposed formulation allows the initial three-dimensional problem to be reduced to a two-dimensional unit cell involving only one wire, well suited for fast computations of contact problems and dispersion curves. The existence of wave modes along the two directions (screw axis and circumferential direction) is justified from a theoretical point of view by considering the metric tensor of a mixed twisting-polar coordinate system. Numerical results are presented for a typical armor of power cable, focusing on longitudinal waves propagating predominantly inside the wires. The internal part of the cable is approximated as a homogenized medium to preserve the continuous screw symmetry of the problem. A comparison with experimental measurements is carried out. The results show that the modal velocity of longitudinal waves behaves as in a single free wire above a limit frequency identified by the model. This is not the case of modal attenuation, always greater in the armor due to mechanical contact with the viscoelastic sheaths. Two modes of potential interest for the non-destructive evaluation of armors are identified. The influence of mechanical contacts on wave propagation in armors is finally discussed, including interwire contact.

中文翻译：

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螺旋多线铠装中的弹性导波

在本文中，提出了一种数值方法来研究弹性导波在保护圆柱形结构（例如电缆和管道）的装甲中的传播，并评估在无损评估和结构健康监测的背景下使用这些波的可行性. 装甲通常由大量与围绕结构的聚合物护套接触的螺旋线组成。数值方法结合了用扭曲坐标编写的半解析有限元方法，它说明了问题沿结构轴的连续螺旋对称性，以及横截面中的旋转布洛赫条件，以说明问题的高阶离散圆对称。所提出的公式允许将最初的三维问题简化为仅涉及一根导线的二维单位单元，非常适合快速计算接触问题和色散曲线。通过考虑混合扭转-极坐标系的度量张量，从理论角度证明沿两个方向（螺旋轴和圆周方向）存在波模式是合理的。给出了典型电力电缆铠装的数值结果，重点关注主要在电线内部传播的纵波。电缆的内部部分近似为均质介质，以保持问题的连续螺旋对称性。进行与实验测量的比较。结果表明，纵波的模态速度在模型识别的极限频率以上表现为单根自由线。这不是模态衰减的情况，由于与粘弹性护套的机械接触，装甲中的衰减总是更大。确定了装甲无损评估的两种潜在兴趣模式。最后讨论了机械接触对装甲中波传播的影响，包括线间接触。