A major challenge in the vibration performance assessment of structures under crowd jumping loads is the lack of efficient prediction models. With the challenge in mind, this study develops a multi-mode response spectrum for multi-harmonic crowd jumping loads to predict the root mean square value of structural accelerations according to the stochastic vibration theory. The response spectrum is applicable to structures with arbitrary vibration modes, because crowd jumping loads are regarded as multi-point excitations. A random field model proposed by the author is used to derive the closed-form expression of the single-mode response induced by individual jumping loads of a single-harmonic. Furthermore, the closed-form expressions of the correlation coefficients for different load harmonics, different vibration modes, and different jumping persons are established based on the random field model. The performance of the response spectrum is evaluated for two floors, and the results indicate the feasibility of the proposed approach to predicting structural accelerations subjected to crowd jumping loads.

人群跳跃载荷下结构振动性能评估的主要挑战是缺乏有效的预测模型。考虑到这一挑战，本研究开发了多谐波人群跳跃载荷的多模态响应谱，以根据随机振动理论预测结构加速度的均方根值。响应谱适用于具有任意振动模式的结构，因为人群跳跃载荷被视为多点激励。采用作者提出的随机场模型，推导出单次谐波的单个跳跃载荷引起的单模响应的闭式表达式。此外，不同载荷谐波、不同振动模式的相关系数的闭式表达式，并基于随机场模型建立不同的跳跃者。对两层楼的响应谱性能进行了评估，结果表明所提出的方法在预测人群跳跃载荷下的结构加速度方面的可行性。