Treyssède F, Laguerre L, Cartraud P, Soulard T
GERS-GeoEND, Univ Gustave Eiffel, IFSTTAR, F-44344 Bouguenais, France.
GERS-GeoEND, Univ Gustave Eiffel, IFSTTAR, F-44344 Bouguenais, France.
Ultrasonics. 2021 Feb;110:106294. doi: 10.1016/j.ultras.2020.106294. Epub 2020 Nov 9.
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.
本文提出了一种数值方法，用于研究弹性导波在保护圆柱形结构（如电缆和管道）的铠装层中的传播，并评估在无损检测和结构健康监测背景下使用这些波的可行性。铠装层通常由大量与围绕结构的聚合物护套接触的螺旋线组成。该数值方法将用扭转坐标编写的半解析有限元方法与横截面中的旋转布洛赫条件相结合，前者考虑了沿结构轴的连续螺旋对称性，后者用于考虑离散圆对称性的高阶特性。所提出的公式允许将初始三维问题简化为仅涉及一根导线的二维单元，非常适合快速计算接触问题和频散曲线。从理论角度通过考虑混合扭转 - 极坐标系统的度量张量来证明沿两个方向（螺旋轴和圆周方向）存在波模。给出了典型电力电缆铠装层的数值结果，重点关注主要在导线内部传播的纵向波。电缆内部部分近似为均匀介质以保持问题的连续螺旋对称性。并与实验测量结果进行了比较。结果表明，纵向波的模态速度在模型确定的极限频率以上的表现与单根自由导线中的情况相同。模态衰减情况则不同，由于与粘弹性护套的机械接触，铠装层中的模态衰减总是更大。确定了两种对铠装层无损检测可能有意义的模式。最后讨论了机械接触对铠装层中波传播的影响，包括线间接触。
