MSCA-COFUND-CLEAR-Doc-PhD Position#CD22-45: Modeling elastic wave propagation in wire ropes in view of health monitoring

Context:

Cables play a key role in urban and suburban mobility. They are to be increasingly used in the infrastructures of traditional and future transportation (urban cable-ways, crossing works, ...). In order to prevent risks due to aging, mechanical guided waves have the potential to be employed to inspect cables in parts that are inaccessible to magnetic, local methods based on flux leakage — for example at anchoring areas [1]. These waves also have the potential to monitor large parts in real time.

Requirements and challenges of modeling:

Guided waves are multimodal and dispersive, that is, their number and speeds depend on the frequency. Propagation models are essential to optimize an instrumentation, interpret measurements, predict sensitivity to given defects and feed advanced inversion schemes able to detect and characterize these defects. Among other aspects, modeling must properly account for the helical geometry of cables and inter-wire contacts. Indeed, contacts play an important role in wave propagation and give rise to phenomena that depend on the tensile (static) state of the cable. First reported on a seven-wire strand [2], these phenomena are now well understood thanks to a model based on a finite element representation of the cross-section of each wire [3]. However, this modeling approach is expensive in terms of degrees of freedom and is thus limited to cables made of few wires (a single strand or a bi-layered cable) or to cables whose specific symmetries enable to drastically reduce the size of the mesh. To date, no modeling method can be applied to multi-layered or multi-stranded cables - such as those used for overhead transmission lines or for cable-ways. This is the challenge that the thesis proposes to meet.

Project:

This thesis aims at extending the state of the art in mechanical waves modeling to cables made of many wires, and then supporting the development of monitoring methods to prevent risks related to the aging of cables. More specifically, the focus is set on multi-layered and multi-stranded cables.

To achieve the required drastic reduction in the number of degrees of freedom — two to three orders of magnitude are expected — this thesis proposes to adopt a simplified representation of the wires by means of beam elements coupled by quasi-static springs whose stiffnesses derive from Hertz’s law. Such formulas are well-known for non-parallel wires in contact (point contacts). For the line contacts occurring between the core and peripheral wires of a strand, the thesis will exploit formulas recently derived by neglecting the effect of curvature on the contact stiffness [4].

Thus, the proposed modeling approach combines two points of view:

–in the cross-section: inspiration is taken from the field of granular media to establish the contact stiffnesses and use them in the mark of beam theory;

–in the axial direction: inspiration is taken from the field of periodic media (the periodicity stems from the helical structure of cables) to determine the geometry of the irreducible unit-cell and to numerically obtain the related Bloch waves.

The proposed models will be validated experimentally by relying on existing equipment at the host laboratory (piezoelectric and/or EMAT transducers, tensile bench, ...).

Objectives:

- To model elastic wave propagation at reduced costs by accounting analytically for contacts, at a given known static state.

- To verify the hypotheses by comparing with a reference model (finite elements) on (A) a known case (a seven-wire strand), and then on (B) an intermediate case (a bi-layer cable).

- To compare the predictions of the new model to experiments (case (B)) focused on the first higher order guided modes, whose characteristics depend highly on inter-wire contacts.

- To demonstrate the applicability of the new approach on (C) a case that is out of reach for established methods (a multi-stranded cable).

References:

[1] L. Laguerre, O. Durand, R. Colin, 27 oct. 2020, Method for detecting a defect in a metal wire of a set of metal wires, in particular for an anchoring area of a civil engineering structure. U.S. Patent No 10,816,511

[2] H. Kwun, K.A. Bartels, J.J. Hanley, 1998, Effects of tensile loading on the properties of elastic-wave propagation in a strand, Journal of the Acoustical Society of America, 103, pp. 3370-3375

[3] F. Treyssède, 2016, Dispersion curve veering of longitudinal guided waves propagating inside prestressed seven-wire strands, Journal of Sound and Vibration, 367, pp. 56-68

[4] P. Mora, F. Treyssède, and L. Laguerre, Cables are elastic waveguides with granular cross section, CFM 2022 – 25ème Congrès Français de Mécanique, Aug 2022, Nantes, France