Abstract
For human assembly structures in which the mass of the crowd is significant compared to that of the structure, it is necessary to model the passive crowd as a dynamic system added to the main structural system. Earlier work by the authors has analysed the frequency response of a joint crowd-structure system in which the structure is treated as a single degree-of-freedom (SDOF) system and the seated and standing crowds are each modelled as a two degree-of-freedom (2DOF) system. It was found that the occupied structure has dynamic properties different to the empty structure. This paper investigates representing the joint crowd-structure system as an equivalent reduced-DOF system that would have the advantage of simplifying the analysis. The modal properties of the equivalent reduced-DOF system, if known, can give a useful indication of how the passive crowd affects the modal properties of the occupied structure. Two equivalent reduced-DOF systems are investigated – SDOF and 3DOF systems. The errors between the responses of the equivalent systems and the full model are calculated and presented in the paper. The results show that the full model exhibits the behaviour of a SDOF system for structures with natural frequencies less than 4 Hz (when empty), whereas for structures with natural frequencies above 4 Hz the equivalent 3DOF system gives a better fit to the full model.