Interaction of guided waves with defects in a multilayered cylinder by an asymptotic approach

Abstract

This work deals with the problem of the propagation of an elastodynamic field radiated by a source in a cylindrical layered medium which interacts with and is diffracted by a defect. At low frequencies, where the defect size is much smaller than the wavelength, this interaction can be approximated by a point source, located at the defect position. This secondary source is expressed by the Green function and its derivative. The Green function, which describes the response of an undamaged cylinder, is calculated using the canonical form of the wave equation initially expressed as a function of the spatial and temporal variables. Performing the Laplace in time and Fourier transforms along the cylinder axis, this equation is written as an ordinary differential equation with respect to the radial position. The solution for the transversely isotropic case is obtained by adopting the partial wave formulation, expressed as a combination of the modified Bessel's functions of the first and second kind. Having assembled the layers, numerical inverse transforms are performed to obtain the real wave fields. This technique allows for reduced computational costs and faster calculation times and could be used for the non destructive testing of embedded pipes and tubes.