A Time-Domain Finite-Difference Method for Bending Waves on Infinite Beams on an Elastic Foundation

Abstract

To model the vibration and structure-borne sound excitation and propagation of a railway rail, it can be modeled as an infinite beam on an elastic foundation. Existing analytical or numerical models are either formulated in the frequency domain or consider only finite beams in the time domain. Therefore, a time-domain approach for bending wave propagation on an effectively infinite beam on an elastic foundation is proposed. The approach makes use of an implicit finite-difference method that allows for varying properties of the beam and the foundation along the length of the beam. Strategies for an efficient discretization are discussed. The method is validated against existing analytical models for a single layer and two layers, as well as continuous and discrete support. The results show very good agreement, and it can be concluded that the proposed method can be seen as a versatile method for simulating the behavior of a beam on different kinds of elastic foundations.