Accuracy of semi-analytical finite elements for modelling wave propagation in rails

Abstract

The semi-analytical finite element method (SAFE) is a popular method for analysing guided wave propagation in elastic waveguides of complex cross-section such as rails. The convergence of these models has previously been studied for linear triangular elements. This paper extends this study to include quadratic triangular elements and other linear and quadratic elements. It is shown that for a given number of degrees of freedom the quadratic elements are more efficient than the linear elements. Based on the results of the convergence studies presented here, the use of quadratic quadrilateral elements is recommended and these may be complemented by quadratic triangular elements if necessary. The use of symmetry and antisymmetry boundary conditions when modelling rails was also investigated. It was found that these models predict all the modes of propagation within the frequencies investigated. The use of this approach is therefore recommended for elastic waveguides with symmetrical crosssection.