A Piecewise Stationary Spectral Model for Walking Crowd–Structure Interaction

Pedestrian-induced vibration is a critical serviceability concern for flexible structures such as footbridges and long-span floors. Existing human–structure interaction models commonly rely on single-degree-of-freedom simplifications and time-domain simulations, making them less suitable for frequency-domain analysis. This paper proposes a spectral analysis model for crowd-structure interaction vibration under unrestricted pedestrian traffic. The structure was formulated as a multi-degree-of-freedom modal system, whereas each pedestrian is represented by an independent spring–mass–damper system. To address the time-varying nature of moving crowds, a piecewise stationary assumption was introduced: the continuous walking path was discretized into fixed position groups, within each of which a time-invariant coupled equation of motion was established. The response spectra obtained for different position groups were combined using residence-time weighting, thereby allowing nonuniform walking speeds to be considered. The corresponding frequency response function was derived using the state–space method, and the structural acceleration power spectral density and root mean square responses were obtained by incorporating an unrestricted crowd walking load spectral model. Comparisons with field measurements from two footbridges demonstrated reasonable agreement. The resulting framework offers an efficient frequency-domain approach for vibration serviceability assessment under unrestricted pedestrian traffic.