Exploration of active human–structure interaction during rhythmic jumping

Abstract

This work presents a mathematical formulation for active human–structure interaction during rhythmic vertical jumping. The structure is represented by a single-degree-of-freedom (SDOF) nonlinear oscillator with cubic stiffness, while the jumper is modeled as a harmonically excited spring-mass-damper (SMD) system whose stiffness varies with the jump frequency. A piecewise-smooth contact dynamics formulation is used to allow the loss of contact between the jumper and the structure. Numerical simulations investigate how variations in propulsion force ratio, damping, and jump frequency influence the response of the coupled system on both non-resonant and resonant structural models. The results show that larger propulsion force values, combined with lower damping ratios, can lead to period-doubling and chaotic motions, whereas higher human damping mitigates these nonlinear effects. With moderate propulsion force levels, the system exhibits responses consistent with experimental results reported in the literature. At lower frequencies, softening bifurcations produce larger displacements for the jumper, while higher frequencies suggest new jumping strategies. When a resonant structural model is considered, the system exhibits sub-harmonic, high-order and chaotic responses driven by the interaction between piecewise leg stiffness and the structures’s cubic non-linearity. These regimes delineate frequency and propulsion force bands that, once further calibrated, can inform preliminary assessments of lightweight floors susceptible to human-induced vibrations.