The application of finite element modelling to guided ultrasonic waves in rails

There has been a rapid growth of interest in the use of guided ultrasonic waves for large-scale screening of components, predominately pipes, for corrosion((1,2)). These waves are analogous to Lamb waves in plates and exhibit dispersive behaviour An important factor in enabling these waves to be used for non-destructive testing is knowledge of the dispersive properties, ie the variation of wave velocity with frequency, for a given component. This is presented in graphical form as a dispersion curve. An innovative numerical method for the calculation of dispersion curves of any prismatic section is proposed. To date, dispersion curves have been generated by solving analytical equations. However as far as is known, there are no analytical solutions available for components with irregular cross-sections, such as rails. Dispersion curves for a rectangular steel bar and a steel rail are presented in this paper. Dispersion curves are essential information for the development of long-range ultrasonic inspections systems and the new, technique opens up the possibility of developing a long-range ultrasonic inspection system for components with irregular cross-sections, such as rails. The method described in this paper has been validated against available analytical solutions for simple geometries. The results from the numerical technique were found to agree closely with analytical solutions. An experiment has been carried out in a rectangular steel bar anti predicted arrival times of the propagating waves have been found to agree with the times calculated using the group velocity dispersion curve obtained.