Certain numerical issues of wave propagation modelling in rods by the Spectral Finite Element Method

In the presented work various problems related with the accuracy of wave propagation modelling by the use of the Spectral Finite Element Method have been discussed and investigated. The results presented in the current study have been obtained for rod structural elements, however, in the opinion of the authors the general conclusions that can be made based on these results are also valid for other types of structural elements used for wave propagation problems. The paper addresses various numerical aspects influencing appropriate modelling of wave propagation in rod structural elements. The results of numerical simulations obtained by the authors and related with the use of single-mode, two-mode and higher order rod behaviour theories are discussed and studied in details. The influence of such parameters as node distribution within elements, the order of approximation polynomials, inertia matrix diagonalisation, and more, all related with numerical problems concerned with wave propagation in rods have been carefully analysed in terms of their impact on appropriate modelling of the wave propagation phenomena.