Parametric study of modal properties of damped two-degree-of-freedom crowd–structure dynamic systems

This paper investigates numerically the modal properties of damped 2-degree-of-freedom (d.o.f.) representations of crowd-occupied civil engineering structures, such as grandstands. In particular, it attempts to explain observations of some curious changes in natural frequencies and damping in measurements made by other researchers in the past when such structures were occupied compared with when they were empty. Natural frequencies, mode shapes, modal masses and damping ratios are examined parametrically for a range of ratios of frequency, mass and damping coefficients of two single-d.o.f. systems connected in series representing the ‘human’ and ‘structural’ vibration behaviour. It is found that a damped 2-d.o.f. model of a crowd–structure system can explain (1) damping increases, (2) additional modes of vibration and (3) increases as well as decreases of natural frequencies observed on real-life grandstand structures due to crowd occupation. Therefore, a mathematical framework for simplified dynamic response analysis of assembly structures based on equivalent 2-d.o.f. dynamic modelling of crowd–structure interaction may be a prudent way forward.