A methodology is proposed to investigate guided waves in curved structures. In a general framework, the existence of guided modes is discussed in curved waveguides. Translational invariance, implicitly used for the analysis of straight waveguides, is redefined for curvilinear coordinate systems. We show that a helical coordinate system fulfills the invariance property for any physics. Then our study focuses on elastic waves. Owing to the difficulty in achieving analytical solutions, a numerical approach based on the so-called semi-analytical finite element is adopted. Civil engineering cables constitute the main application of this work. The basic component of cables is usually a helical structure composed of several wires. This multi-wire characteristics further complicates the analysis of guided waves. We show that a twisting coordinate system allows to satisfy translational invariance in seven-wire strands. A model is also proposed in order to account for prestressing effects. Finally, other complicating effects in cables are briefly discussed (presence of embedment, wave scattering by defects).
Investigation of guided modes in helical structures: understanding wave propagation in civil engineering cables