This thesis is devoted to the modeling of elastic wave propagation in helical waveguides subjected to axial loads. Non destructive testing (NDT) of springs and multi-wire strands is a potential application of the proposed model. The study of wave propagation in loaded helical waveguides requires the expression of tridimensional equations describing the motion of prestressed structures in a helical coordinate system. The semi-analytical finite element method (SAFE) is then applied considering the property of translational invariance and the problem is reduced to the cross-section (2D). The eigenproblem obtained can be solved by fixing the wavenumber or the frequency. The computation of the prestressed static state is solved by a helical homogenization method accounting for the invariance. The correlation between the static computational model and an analytical model of the literature indicates the validation of our model for springs. Moreover, agreement between our model and a 3D finite element model found in the literature for the case of seven-wire strands is satisfactory. The SAFE model is validated with a model of Timoshenko helical beams subjected to axial loads. It is shown that wave propagation is sensitive to axial loads in terms of prestress and geometry deformation and that this influence is significant only at low frequencies. Finally, the elastic wave propagation in seven-wire strands subjected to axial loads is analysed. The dispersion curves obtained numerically are compared to experimental data in the literature. A good agreement is found for the first compressional-like modes and their veering central frequency.
