Analysis of Guided Wave Behaviour in Rails Using Numerical or Analytical Models

The vibration of rails is a major contributor to railway rolling noise, and consists of different guided waves that propagate along the rail. To study the dynamic behaviour of a railway track, models based on the Timoshenko beam theory and the waveguide finite-element method were established. The solution procedures to obtain the free wave response and the forced response for each model were determined. The characteristics of guided waves in rails, such as wavenumber, group velocity, mobility, and decay rate, were analysed based on two different models. The waveguide finite-element model, which includes all the features of rail cross-section deformation, makes it possible to identify eight kinds of guided waves in rails within a frequency range of as much as 6 kHz. Moreover, the phenomena of wave mode exchange and group velocity exchange between waves are discussed, as well as the peak in the mobility caused by the excitation of the higher-order wave mode. The Timoshenko beam model can identify five of these wave modes, including those for bending, torsion, and extensional waves, but it cannot identify the ones associated with cross-section deformations that cut on at frequencies of more than 1.5 kHz. The Timoshenko beam model provides acceptable results for point mobilities of as much as 2 kHz.