A modified hybrid Van der Pol/Rayleigh model for the lateral pedestrian force on a periodically moving floor

Abstract A single degree of freedom self-sustained oscillator is proposed in order to model the lateral oscillations of a pedestrian walking on a periodically moving floor and particularly on a shaking table. In a previous work, the authors have shown that a suitable form for the restoring force of such an oscillator corresponds with a modified hybrid Van der Pol/Rayleigh (MHVR) model, whose associated parameters have been identified in the autonomous (rigid floor) case for a group of twelve pedestrians. The MHVR oscillator is analyzed here for the non-autonomous case, where the moving floor is subjected to a harmonic excitation. It has been experimentally proven that in this case the pedestrian may change his (her) natural walking frequency and synchronize with the floor oscillation frequency: one says that the so-called “frequency entrainment” occurs. This means that, under certain conditions, the response frequency switches from the natural value to that of the external excitation. This paper discusses the steady “entrained” response of the MHVR model subjected to a harmonic excitation, in terms of response amplitude curves obtained using the Harmonic Balance Method. Experimental results available in the literature and involving pedestrians walking on a shaking table are compared with the model predictions for illustrative purposes.

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