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


Job Information

Université Gustave Eiffel
Research Field
Engineering » Mechanical engineering
Physics » Acoustics
Mathematics » Applied mathematics
Researcher Profile
First Stage Researcher (R1)
Application Deadline
Type of Contract
Job Status
Hours Per Week
Is the job funded through the EU Research Framework Programme?
H2020 / Marie Skłodowska-Curie Actions COFUND
Marie Curie Grant Agreement Number
Is the Job related to staff position within a Research Infrastructure?

Offer Description


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.


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, ...).


- 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).


[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


Research Field
Education Level
Bachelor Degree or equivalent
Research Field
Education Level
Bachelor Degree or equivalent
Research Field
Education Level
Bachelor Degree or equivalent
  • At the time of the deadline, applicants must be in possession or finalizing their Master’s degree or equivalent/postgraduate degree.
  • At the time of recruitment, applicants must be in possession of their Master’s degree or equivalent/postgraduate degree which would formally entitle to embark on a doctorate.
Specific Requirements
  • You must hold a graduate degree in the field of mechanics, acoustics or applied mathematics. An experience in finite element modeling would be appreciated.
  • You will be joining a multi-disciplinary group with whom you will have to be able to interact.
  • You must be highly motivated by research, theoretical work, developing and using scientific calculation codes (Python/Matlab), as well as comparing and questioning results against experimental data.
  • You must have knowledge of scientific English good enough to communicate results in international peer-reviewed journals and conferences.
  • No knowledge of French is required. Several months’ travel abroad is to be expected.

Additional Information

  • High-quality doctoral training rewarded by a PhD degree, delivered by Université Gustave Eiffel
  • Access to cutting-edge infrastructures for research & innovation.
  • Appointment for a period of 36 months based on a salary of 2 700 € (gross salary per month).
  • Job contract under the French labour legislation in force, respecting health and safety, and social security: 35 hours per week contract, 25 days of annual leave per year.
  • International mobility will be mandatory
  • An international environment supported by the adherence to the European Charter & Code.
  • Access to dedicated CLEAR-Doc trainings with a strong interdisciplinary focus, together with a Career development Plan.
Eligibility criteria

Applicants must fulfil the following eligibility criteria:

  • At the time of the deadline, applicants must be in possession or finalizing their Master’s degree or equivalent/postgraduate degree.
  • At the time of recruitment, applicants must be in possession of their Master’s degree or equivalent/postgraduate degree which would formally entitle to embark on a doctorate.
  • At the time of the deadline, applicants must be in the first four years (full-time equivalent research experience) of their research career (career breaks excluded) and not yet been awarded a doctoral degree. Career breaks refer to periods of time where the candidate was not active in research, regardless of his/her employment status (sick leave, maternity leave etc). Short stays such as holidays and/or compulsory national service are not taken into account.
  • At the time of the deadline, applicants must fulfil the transnational mobility rule: incoming applicants must not have resided or carried out their main activity (work, studies, etc.) in France for more than 12 months in the 3 previous years.
  • One application per call per year is allowed.
  • Applicants must be available full-time to start the programme on schedule (November 1st 2023).
  • Application rules are enforced by the French doctoral system which specifies a standard duration of 3 years for a full-time PhD together with the MSCA standards and the OTM-R European rules as follows.
  • Citizens of any nationality may apply to the programme.
  • There is no age limit.
Selection process

Please refer to the Guide for Applicants available on the CLEAR-Doc website:

Additional comments
  • The First step before applying is contacting the PhD supervisor. You will not be able to apply without an acceptation letter from the PhD supervisor.
  • International mobility planned: Please contact your PhD supervisor.
  • Please contact the PhD supervisor for any additional detail on job offer.
  • There are no restrictions concerning the age, gender or nationality of the candidates. Applicants with career breaks or variations in the chronological sequence of their career, with mobility experience or with interdisciplinary background or private sector experience are welcome to apply.
  • Support service is available during every step of the application process by email:
Website for additional job details

Work Location(s)

Number of offers available
Université Gustave Eiffel
Postal Code
Allée des Ponts et Chaussées


5, Boulevard Descartes
Postal Code