Study of the Ground Reaction Force Induced by Swaying or Bobbing People and its Dynamic Effect on Loaded Structures

The core of the submitted article is in the modeling of bobbing people for describing the action of qualified vandals, who try to achieve an excessive level of vibration by their periodic sway in the knees while they are not losing contact between the footbridge deck and their feet. The DLF models, which already exist, provide particular coefficients only for specific pacing frequencies. On the other hand, our study presents DLF coefficients as a continuous function for frequencies in the range of 1 Hz – 3 Hz. The newly presented DLF model is based on the measurement of 15 random people and compared with the experimental data. Each of these people was measured by a force plate in the frequency range of 1 Hz – 3 Hz. Since we know who exactly was present during the experiment, we also monitored the contact forces produced by these people at frequencies identical to some natural frequencies of the footbridge according to the experimental setup. These measured forces were used directly as the input into the calculation process and compared with the experiment too. Subsequent dynamic calculations of the forced vibration were carried out by Modal Decomposition Method. This method requires a mode shape as one of the inputs, these mode shapes were calculated by the Subspace Iteration Method using commercial software Dlubal RFEM 5.03. Numerical integration of the equations of motion (forced vibration analysis) was done by self-written MATLAB codes and routines. At the end of the article, we summarize the results of theoretical dynamic analysis obtained by theoretical modeling of these vandals. The main outcomes are in the determination of the continuous functions for DLFs and their phase angles based on the experimental results. These values are crucial e.g. for designers, who need to compute the response of a footbridge or a grandstand which could be excited by swaying or bobbing vandals or spectators. Obtained and evaluated continuous functions for DLFs were compared by literature where researchers presented some DLFs for discrete sets of frequencies, which produced a good level of accordance.