跳跃荷载的功率谱模型研究

Power spectral density model for human jumping load

跳跃荷载的傅里叶级数模型基于周期性假定,忽略了跳跃过程的本质随机性,影响人致结构振动分析的准确性。文中研究将跳跃荷载视为窄带平稳随机过程,基于73人次334条试测荷载样本建立单人跳跃荷载的功率谱模型,经跳跃频率和阶数归一化后可采用两个高斯函数的和表示,分别反映跳跃能量的集中和扩散程度,模型参数则根据其总能量与实测功率谱能量相等的原则得到。进一步结合随机振动理论,提出由跳跃功率谱预测结构在单人跳跃荷载作用下任意位置加速度峰值响应的计算方法和步骤。理论预测结果与楼板模型的试验结果对比表明,所建议的功率谱模型的计算结果合理,可用于跳跃荷载作用下结构响应的计算与分析。最后,讨论基于功率谱模型的人群跳跃荷载作用下结构响应的计算方法。

Fourier series model has been widely used to represent human jumping load. This model, however, ignores the randomness in human jumping process, which may lead to uncertainties in the prediction of structural response. In this study, the human jumping load is viewed as a narrowband stationary stochastic process, and then the power spectral density （PSD） model is developed based on 334 experimental jumping load records from 73 test subjects. The PSD model was firstly derived from the measured records. A non-dimensional PSD model can be expressed by the summation of two Gaussian functions normalized from the jumping frequency and the rank order, which reflect the concentration extent and the distribution extent of jumping energy, respectively. Model parameters can be determined by equating the total energy of the proposed PSD with that of the measured PSD. In combination with the stochastic vibration theory, the computational method and steps for predicting the peak acceleration at an arbitrary location of floor were proposed. The predictions for an experimental floor model subjected to individual jumping were compared with measured peak responses. The comparison between the theoretical predictions and the experimental results indicates that the proposed PSD function is applicable for predicting the floor＇s response to individual jumping. Finally, the computational framework of evaluating crowd-induced structure vibration was also discussed.