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Crowd jumping loads are often simplified to a single-point excitation in the existing Fourier series-based models, most of which lack the data support of crowd jumping experiments. A Fourier series-based multi-point excitation model for crowd jumping loads is herein developed, where two parameters, the jumping frequency, and the time lag shift, are selected to quantify the crowd synchronization. After the verification of 3D motion capture technology, the probability distributions of the jumping frequency and the time lag shift are modeled based on the crowd jumping experiment, in which the trajectories of the reflective markers of 48 test subjects were simultaneously recorded by 3D motion capture technology. Through repeated sampling, the jumping load of each person in a crowd is simulated. This model could offer a useful method for evaluating the vibration performance of assembly structures like grandstands, gymnasiums, and concert venues. [ABSTRACT FROM AUTHOR]

Existing dynamic load factors (DLF) for crowd jumping loads are modeled by identifying the peaks and energies from the corresponding Fourier amplitude spectrum, which may underestimate and overestimate structural responses, respectively. Based on the principle of equal structural responses, this study herein develops an equivalent DLF, using the frequency response function to weight and integrate the power spectral density (PSD) matrix of crowd jumping loads. Firstly, massive PSD matrices of different crowd sizes and different metronome frequencies are simulated using a random field model of crowd jumping loads. Thereafter, the equivalent DLF of different structural damping ratios, crowd sizes, metronome frequencies, and non-exceedance probabilities are investigated, and a model of the equivalent DLF is established accordingly. It is believed that this model could provide an efficient and accurate way to conduct reliability design for structures subjected to crowd jumping loads. [ABSTRACT FROM AUTHOR]

Severe vibrations may occur on slender structures like footbridges and cantilever stands due to human-induced loads such as walking, jumping or bouncing. Currently, to develop a load model for structural design, the main features, such as periodicity and stationarity of experimental load records, are artificially extracted and then mathematically modeled. Different physical features have been included in different load models, i.e. no unified load model exists for different individual activities. The recently emerged generative adversarial networks can be used to model high-dimensional random variables. The probability distribution of these variables learned from real samples can be used to generate new samples, avoiding extracting features artificially. In this paper, a new model is proposed which combines the conditional generative adversarial networks and Wasserstein generative adversarial networks with gradient penalty to generate individual walking, jumping and bouncing loads. The generator of the model has five fully connected layers and a one-dimensional convolutional layer, and the discriminator has five fully connected layers. After one million training steps using the experimental records, the generator can generate high-quality samples similar to real samples in waveform. Finally, by comparing the power spectral densities and single degree of freedom system's responses of the generated samples with real samples, it is further proved that the proposed generative adversarial network model can be used to simulate various human-induced loads. Source code of the model along with its trained weights is provided to the readers to further analysis and application. [ABSTRACT FROM AUTHOR]

Modern slender structures such as long-span floors and cantilever stands are sensitive to jumping-induced vibrations. A conventional deterministic Fourier series model for the human jumping load may overestimate a structure's responses in resonance condition. This paper suggests a power spectral density (PSD) function for the individual jumping load, which was treated as a narrowband stationary stochastic process. Experiments were conducted on individual jumping loads resulting in 334 records from 73 subjects. Statistical analysis of the records led to experimental PSD curves on which a symmetrical bilinear function was suggested. The proposed PSD function is centered on the given jumping frequency and its integer multiples. The function's parameters were determined by equating the total energy of the proposed PSD with that of the experimental PSD. Application of the proposed PSD for predicting a floor's peak response via the stochastic vibration theory was then presented. The predictions for an experimental floor model subjected to individual jumping were compared with the measured peak responses. The comparisons demonstrated that the proposed PSD function was applicable for predicting the floor's response to individual jumping. Finally, the framework for calculating crowd-induced structure vibrations using the suggested PSD was also discussed. [ABSTRACT FROM AUTHOR]