A semianalytical finite element method for elastic guided waves propagating in helical structures

Abstract

Steel multiwire cables are widely used in civil engineering as load-carrying members. The basic element of these cables is usually a simple straight strand made of a straight core and one layer of helical wires. Several difficulties arise in the understanding of guided ultrasonic waves in such structures, partly due to the helical geometry and the interwire coupling effects. In the context of nondestructive evaluation, this paper aims at theoretically investigating the propagation of elastic waves in helical waveguides. A numerical method is chosen based on a semianalytical finite element technique that relies on a specific nonorthogonal curvilinear coordinate system. This system is shown to be translationally invariant along the helix centerline so that a spatial Fourier transform can be explicitly performed along the axis and the problem is reduced to two dimensions. A single helical wire is first considered. The convergence and accuracy of the proposed method are assessed by comparing finite element results with reference solutions. The method is then extended to study a seven wire cable with simplified contact conditions. Dispersion curves are presented for wave numbers as well as energy velocities. Significant differences with the infinite straight cylinder are observed.