Elastic guided waves in a spiral wire rope: Theory and modeling

Elastic guided waves are of great interest for the non-destructive evaluation of cables. However, accurately modeling wave propagation in these structures requires complex numerical models that account for their helical, multi-wire geometry and the effects of prestress due to high tension loads. This paper provides a theoretical and computational framework for studying wave propagation in spiral ropes, also known as spiral strands, consisting of a central wire surrounded by two layers of helical wires. These layers are typically wound in opposite directions, breaking continuous symmetry and introducing both line and point interwire contacts. Using a non-trivial curvilinear coordinate system, termed bi-helical, this paper establishes the existence of wave modes in such structures, defines the three-dimensional repetitive unit cell of the spiral rope, and implements a specific Bloch–Floquet wave finite-element method to solve the wave propagation eigenproblem along bi-directional helical coordinates. Interwire contact areas and their dependence on tensile loads are approximated through geometric interpenetrations governed by Hertzian contact laws. The proposed method is validated through numerical experiments on reference test cases, including a cylinder, a seven-wire strand, and a special spiral strand exhibiting translational symmetry. Finally, dispersion curves are presented for various two-layered spiral strands, considering different helix angles and tensile loads. The results reveal complex wave behavior, characterized by multiple veerings strongly influenced by contact areas, paving the way for future experiments and practical applications in the non-destructive evaluation of cables.