Multimodal dispersive waves in a free rail

Abstract

In this paper, we present a solution method based on finite element (FE) modeling to predict multimodal dispersive waves in a free rail. As well as the modal behaviors and wavenumber-frequency dispersion relations, the phase and group velocities of six types of propagative waves are also derived and discussed in detail in the frequency range of 0–5 kHz. To experimentally distinguish different types of wave modes, the operating deflection shape (ODS) measurement approach is employed in the laboratory. ODS is measured from the spatial distribution of imaginary parts of the FRFs. We also propose a synchronized multiple-acceleration wavelet (SMAW) approach to experimentally study the propagation and dispersion characteristics of waves in a free rail. The group velocities in the vertical, longitudinal and lateral directions are estimated from the wavelet power spectra (WPSs). The good agreement between the simulation and measurement in terms of mode shapes and ODSs, wavenumber-frequency dispersion curves, and group velocities indicates that the ODS and SMAW approaches are capable of distinguishing different wave modes and measuring wave propagation and dispersion characteristics. In situ experimental results further demonstrate the effectiveness of the ODS measurement for coupled modal identification and the SMAW approach for wave dispersion analysis of the rail in a field track.