HIGHER VIBRATION MODES IN RAILWAY TRACKS AT THEIR CUT-OFF FREQUENCIES

Forced vibrations of a railway track excited at the cut-off frequency of one of its wave modes are examined theoretically, numerically and experimentally in the frequency range from 5 to 50 kHz. The background of this paper is the new idea of using the local vibration zone of the rail close to the excitation to detect passing train wheels. An important parameter which influences this local vibration zone is system damping. The determination of a new quality factor to characterize damping of a system which both resonates and interacts with travelling waves is first studied in the case of a beam on a viscoelastic foundation. Some key differences compared with a single-degree-of-freedom (s.d.o.f.) mechanical oscillator are pointed out and an adopted damping measurement method is suggested. The phenomenological behavior of higher vibration modes is then investigated using a model of several elastically connected beams referred to as the multiple-mode model. Modal damping is introduced and the model is studied both in a continuous and in a discretely supported configuration. Both localized and non-localized modes are observed in the latter case. The cut-off frequencies and mode shapes are also determined experimentally at a real test track using a scanning laser interferometer and show good agreement with numerical calculations. The spatial behavior of the measured system response at the test track corresponds well to the effects predicted by the multiple-mode model. Damping measurements are performed and the quality factors of several modes are determined and discussed.