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

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.