Mechanical modeling of helical structures accounting for translational invariance. Part 2 : Guided wave propagation under axial loads

This paper corresponds to the second part of a study that aims at modeling helical structures accounting for translational invariance. In the Part 1 of this paper, the static behavior has been addressed using a helical homogenization approach which provides the stress state corresponding to axial loads. The latter is considered as a prestressed state, for elastic wave propagation analysis in helical waveguides, which is the subject of the Part 2 of this paper. Non destructive testing of springs and multi-wire strands is a potential application of the proposed model. Accounting for translational invariance, the elastodynamic equations of prestressed helical structures yield a 2D problem posed on the cross-section, corresponding to a so-called semi-analytical finite element (SAFE) formulation. For helical springs, the numerical model is validated with an analytical solution corresponding to a Timoshenko beam approximation. It is shown that the influence of the prestressed state is significant at low frequencies. Finally, a seven-wire strand subjected to axial loads is considered. The computed dispersion curves are compared to experimental data. Good agreement is obtained for the first compressional-like modes and their veering central frequency.