Mode coupling of guided elastic waves in wire with weak surface corrugation

Abstract

This analytical study aims to explain the experimental result of the mode coupling of elastic waves in a long circular wire by means of the surface corrugations of the wire. It is assumed herein that the wire is made of ideally homogeneous, isotropic, linearly elastic material and its free surface is subjected to weak and continuous corrugation. On the basis of the weakness of corrugation, the multiple scales are introduced to formulate the problem in a perturbation scheme. It is found, as expected, that the mode coupling does occur as the result of scattering from the corrugated surface at a certain frequency where the two modes have the same phase velocity. Coupled-mode equations which govern the amplitude variation in the coupling are then derived systematically from the compatibility condition. The coupling coefficients depend on the modes involved, the geometrical characteristics of the surface corrugation, and the material constant of the wire. The resultant variation of amplitudes well characterizes the pulse distortion observed in the experiments.