Guided waves are now well established for some applications in the non-destructive evaluation of structures and offer potential for deployment in a vast array of other cases. For their development it is important to have reliable and accurate information about the modes that propagate for particular waveguide structures. Essential information that informs choices of mode, transducer, operating frequencies and interpretation of signals, amongst other issues, is provided by the dispersion curves of different modes within various combinations of geometries and materials.
In order to meet this demand members of the NDT group at Imperial College developed DISPERSE (http://www3.imperial.ac.uk/nde/products%20and%20services/disperse) . This software provides the user with valuable information about the modes which can be propagated in a waveguide such as dispersion curves, energy diagrams and mode shapes for instance. It has been widely and successfully used for many years within the group as well as by academic and industrial researchers around the world, under license agreement.
This notwithstanding, the group always aims to use and provide state of the art techniques and tools to tackle the various problems NDT engineers are confronted with. For this reason, DISPERSE’s capabilities are currently being improved and extended by using a different approach based on the Spectral Collocation Method (SCM) instead of the standard root-finding routines. This method surmounts many of the limitations inherent to root-finding routines based on the Partial Wave Method such as spurious modes when fluid layers are present, missing modes or the so called “large fd” problem.
The figures display some results obtained by the SCM: Above, the dispersion curves for a system of three layers (Steel-Water-Steel) obtained by the SCM (red circles) are compared to those obtained with DISPERSE (solid black lines) showing excellent agreement. The SCM completes all cases, including this one, without the need for user participation in the searching and tracing of the dispersion curves. The SCM also gives as eigenvectors of the problem the corresponding mode shapes (below).