Elastic Guided Wave Propagation in the Prestressed Helical Multiwire Waveguide

Abstract

Studying ultrasonic guided wave modes in multiple steel wires helps extend and apply wave dynamics theory to practical engineering. This research focused on elastic wave propagation for investigating dispersion behavior in a helical waveguide under the prestressed state. For the guided wave theory of one-dimensional propagation, the physical system represented as a curve must satisfy translation invariance. Elastic wave propagation in a helical waveguide was analyzed using the semianalytical finite element (SAFE) method. The scaled Frenet–Serret and twisted basis dispersion curves were analyzed for comparison. The bases were used to define covariant and contravariant bases where the strain and stress tensors were expressed. Then, by proving the translational invariance of the system in the curvilinear coordinates, a Fourier transform of the displacement was deployed to distinguish plane waves based on their wavenumber and reduce the study of the waveguide according to its cross-section. Later, the SAFE method derived from the twisted cylindrical coordinate system was compared with the standard axisymmetric SAFE method. Analysis of an outer steel wire of the seven-wire helical strand was carried out for undamped and damped cases with initial prestress conditions to investigate the dispersion behavior of the helical waveguide. Static analysis of the entire seven-wire helical strand was carried out by considering an initial prestress field, and a finite-element method based on asymptotic expansion theory was used to solve contact stress field calculation. Correspondingly, the proposed method was verified with the classical Machida and Costello calculation theories for calculating the stress field on its respective axial cross-section for each wire. A very complex band diagram needs to be investigated while performing a dynamic analysis of the helical waveguide. The current work introduces the modal filters via the so-called coupling conditions to parse the complex dispersion characteristics. When the SAFE method is used to analyze its dynamic wave properties, the employed coupling condition reduces the degrees of freedom of the system and improves calculation efficiency. Henceforth, the proposed methodology for calculating the prestressed state is the potential health monitoring scheme for a helical multiwire.