Simplified modeling of elastic guided waves in a pre-stressed cable

Elastic waves can be employed to probe the mechanical state of pre-stressed cables and look for defects in critical areas. Contacts between wires have been shown to play a major role in wave propagation by giving rise to tension-dependent phenomena such as anomalous transmission at certain frequencies (the "notch frequency effect"). Here, we present a simplified way of modeling the free propagation of waves at low frequencies by analytically accounting for contacts. Wires are described within beam theory and connected with tension-dependent springs derived from Hertz law. In contrast to point-wise contacts, these line-wise contacts also induce second-neighbor coupling, i.e. they connect wires that are not in direct contact one another. The simplified model is compared with a reference model based on a finite elements representation of the cross section ("SAFE" method). The range of validity in frequency is discussed. The results provide a new interpretation for the first higher order modes in and their dependence with tension in terms of contact resonances. The drastic reduction of numerical costs suggests the method could be applicable to more complex civil engineering cables, composed of many wires.