Phase Difference in Lateral Synchronization of Pedestrian Floors Using a Modified Hybrid Van der pol/Rayleigh Oscillator

The modified hybrid Van der Pol/Rayleigh (MHVR) oscillator was originally proposed by the authors to model the lateral oscillations of a pedestrian walking on a rigid floor and it was shown that for the autonomous case, the MHVR oscillator can correctly fit the experimental data. The case of a pedestrian walking on a laterally moving floor is modeled by a nonautonomous oscillator. The case of a floor subjected to a harmonic lateral motion has been then studied by the authors, with focus on the amplitude and stability of the entrained response, i.e. the response having the same frequency as that of the given periodic excitation. For the nonautonomous (moving floor) case, the main focus of this paper is on the analysis of the phase difference between the oscillator entrained response and the external excitation. Both analytical and numerical calculations have been performed. The approximate analytical method is the harmonic balance method. Then, the model is used to represent the experimental results for the pedestrian lateral oscillations during walking. Comparison is made for the examples along with discussions.