Multi-mode response spectrum for multi-harmonic crowd jumping loads

Abstract

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.