Human–Structure Interaction Under Rhythmic Jumping: Model-Form Effects on Structural and Human Responses

Stationary occupants modify the vibration of lightweight floors and grandstands, yet predicted responses depend on how the stationary human is represented. This study examines model-form effects among a conventional separative model (SM), a reduced integrative model (RIM), and a full integrative model (FIM) under rhythmic jumping. A population standing-human program comprising 55 measured structural frequency-response-function (FRF) datasets, of which 50 were retained after quality control, is combined with a re-analysis of previously acquired standing-and-jumping measurements and a multi-harmonic frequency-domain parametric study. Under matched independent five-parameter calibration, the median complex-FRF normalized root-mean-square error (NRMSE) values were 0.0705, 0.0786, and 0.0738 for the SM, RIM, and FIM, respectively. In contrast, a no-refit RIM inheriting the FIM parameter set gave 0.3196, demonstrating substantial calibration compensation across model forms. The rhythmic-jumping re-analysis further showed that no single formulation provided the closest structural-response prediction across all tested frequencies and response metrics. Over the parametric domain, the maximum structural-response discrepancies relative to the FIM reference were 146.67% and 117.10% for the SM and RIM at 1% structural damping, 43.79% and 42.51% at 3%, and 32.52% and 29.84% at 5%. The corresponding analytical human-coordinate discrepancies reached 135.92% and 101.08%, 46.15% and 40.93%, and 37.87% and 37.85%. At 3% damping, the largest resolved interior critical jumping-frequency shifts were 0.21 and 0.19 Hz for the structural response and 0.20 and 0.14 Hz for the human-coordinate response. Mechanism analyses linked the representative structural and human-coordinate discrepancies to third-harmonic alignment with the upper coupled mode, giving discrepancies of 42.1% and 24.1%, respectively. Robustness checks showed comparatively stable sampled-grid 95th-percentile trends across the FIM population BMR interquartile range and under changes in contact ratio, harmonic truncation, and frequency resolution. The results show that sensitivity to stationary-human model form is output- and resonance-specific: simplified formulations may be useful for screening, but model-form effects become important near lightly damped resonances, prescribed activity frequencies, and threshold-sensitive assessments.