An Arnoldi reduction applied to wave propagation to model railway track vibrations

With metropolis and transport grid densification, results of acoustic impact assessment has a pivotal role in rail network expansion. Indeed, for railway neighbors, the pass-by train noise is a key issue. To evaluate this last, the vibrational response of the railway track is needed.To take into account the cross-section deformation and the infinite length, a waveguide finite element method (WFEM) is used. Periodicity between supports is introduced using the Floquet theorem. Only a generic element between two sleepers is simulated. As support, we consider a half sleeper at each end. This model take advantage to feature the three characteristics of the track: the infinite length, the cross-section deformation and the periodical support. Despite its effectiveness, this model lacks robustness and suffers from numerical issues. In this paper, a new method addressing these problems is presented. The second-order Arnoldi method (SOAR) is used to solve WFEM equations. The SOAR is based on a Krylov approximation in order to reduce problem size. This reduction allows eliminating critical values that induce numerical problems. Moreover, the orthogonal basis created by this method allows improving the robustness of the algorithm.In the last part of the paper, the robustness of the model is studied.