Reproduction of lateral ground reaction forces from visual marker data and analysis of balance response while walking on a laterally oscillating deck

Pedestrians walking on a laterally oscillating structure are known to impose ground reaction forces that contain frequency components at the structural oscillation frequency. These forces arise due to the interaction between the balancing pedestrian and oscillating structure on which they walk. They are therefore often termed self-excited (SE) forces. The dynamic influence of these SE forces is to alter the apparent modal mass and damping of the structure. However, in order to gain a deeper understanding of the root cause of these forces, it is necessary to consider the biomechanical response to base motion, as it is this that ultimately generates the ground reaction force (GRF). This paper presents observations from a test campaign in which subjects walked on a laterally oscillating treadmill. A 3-dimensional motion capture camera system was used to track the position of 31 active markers, placed on each subject during walking tests. A range of frequencies and amplitudes were tested. The initial objective was to employ inverse dynamics to reproduce the GRF. This was successfully validated against the directly measured GRF. Marker data was then used to investigate subject’s balance response to base motion. Data relating to a single subject is presented in detail here. Various observations have been made, the most significant of which are that the underlying cause of the SE GRF was confirmed as resulting from a periodic variation of lateral foot placement position. The frequency of variation was found to be equal to the modulus of the difference between the lateral forcing and oscillation frequencies. The subject’s tendency to alter their gait was induced by a sinusoidally varying inertia force imposed due to the base oscillation. Periodic gait width alteration ceased when the pedestrian’s lateral forcing frequency was matched to the base oscillation frequency, explained by stabilisation of the phase relationship between the forcing and oscillation frequencies. Finally, amplitude modulation was found to be a qualitatively suitable mathematical analogue for the biomechanical behaviour observed.