Exploring interactions between a human rhythmic jumper and an oscillating structure using experimental force–displacement analysis

Human rhythmic jumping is known to induce significant vibrations of civil structures, such as grandstands and footbridges. This has been known to introduce maintenance and serviceability concerns. The dynamic interaction between rhythmic human jumping on an oscillating surface is extremely complex due to both non-smooth, loss of contact, nonlinearities and geometric frequency dependant nonlinearity of the legs. This makes it particularly difficult to successfully characterise. A timber beam was constructed and instrumented to investigate these human-structure dynamic interactions. This was designed to simulate a cantilever tier of a grandstand, with similar natural frequency and damping ratio to the full-scale structure and with a similar mass ratio of a single human to the beam as for a crowd to the full-scale structure. Measurements of accelerations and displacements of both the jumper and beam, and of the contact force between them, were acquired. Testing was performed over a large range of prescribed jumping frequencies above and below the structure's natural frequency. Force-displacement curves of each test subject, during the contact phase of rhythmic jumping, and their evolution over all jumping frequencies tested are studied. Least squares system identification was utilised to identify the apparent leg spring stiffness conceptualised as a piece-wise linear spring-mass model. The coefficients are observed to be highly sensitive to jumping frequency. Comparative analysis between rhythmic jumping on stationary and oscillating surfaces is performed to draw conclusions on the influence of surface configuration on a jumper's mechanics. Important differences in jumping dynamics are observed indicating different nonlinear models are required to successfully characterise human rhythmic jumping for the two loading scenarios.