A modified Fourier model for stochastic jumping loads on rigid floors

Abstract

This paper introduces a modified Fourier model for accurately simulating the induced stochastic dynamic jumping force exerted by an individual during jumping motion on a rigid floor. The contact ratio, pace frequency, and amplification factor are the critical parameters in the force modeling. These parameters are considered as random variables. The mean, standard deviation, and interval of variation for the parameters have been computed based on experimental records of individual jumping force-time history. Correlation analysis indicates that the pace frequency and the contact ratio are weakly dependent variables. Moreover, analysis of experimental data shows that the amplification factor depends on both the contact ratio and pacing frequency. To account for this, the modified amplification factor has been incorporated into a truncated Fourier series to model the continuous rhythmic jumping force. The bootstrap resampling technique has been utilized to capture the inherent randomness in the jumping force. Additionally, successive corrections, in terms of the time difference between the metronome beat frequency and the achieved jumping frequency, have been applied in each load cycle to produce the jumping force. Comparisons between the measured force signals and the model-generated forces demonstrate strong agreement. Finally, the jumping vandal loading is simulated on a steel floor in a finite element model, and the responses for both, i.e., the model and the experimental forces, are compared. The results demonstrate that the proposed jumping force model is simple and can be easily used for the vibration serviceability assessment of structures.