A spectral model for human bouncing loads

Fourier series-based models in the time domain are frequently established to represent individual bouncing loads, which neglects the stochastic property of human bouncing activity. A power spectral density (PSD) model in the frequency domain for individual bouncing loads is developed herein. An experiment was conducted on individual bouncing loads, resulting in 957 records linked to form long samples to achieve a fine frequency resolution. The Welch method was applied to the linked samples to obtain the experimental PSD, which was normalized by the bouncing frequency and the harmonic order. The energy, energy distribution center, and energy distribution shape of the experimental PSD were investigated to establish the PSD model. The proposed model was used to analyze structural vibration responses using stochastic vibration theory, which was verified via field measurements. It is believed that this framework can evaluate the vibration capacity of structures excited by bouncing crowds, such as concert halls and grandstands.