is a parametric study, in which different modal characteristics for the structural system are assumed, and the size of the stationary crowd of people is also varied so as to investigate its influence on magnitudes of structural response. The human-structure interaction model assumed for the study is introduced in section 2, and the section also presents the dynamic characteristics assumed for structures and the stationary crowd. The load model and procedures for computing structural response are outlined in section 3. Section 4 presents the results. 2. THE HUMAN-STRUCTURE INTERACTION MODEL Fig. 1 illustrates the human-structure interaction model assumed for the studies of this paper. The grounded system represents the structural system, which is modelled as SDOF system. The structure carries a stationary crowd of people modelled as a SDOF attached to the structural mass. Fig. 1 Human-structure interaction model It is assumed that the governing mode of the structural system is the first mode of vertical bending. This mode is described by the parameters m1, k1, and c1, representing modal mass, stiffness and damping, respectively. The corresponding parameters for the stationary crowd of people atop the structure are denoted m2, k2, and c2. A load p(t) might be applied to the floor mass bringing the system into vibration. The following equations are assumed to apply: ( )2 2 2 2 2 f k m π = 2 2 2 2 2 ζ c m k = (1) ( )2 1 1 1 2 f k m π = 1 1 1 1 2 ζ c m k = (2) where the set (m1, f1, ζ1) represents the dynamic characteristics associated with the first bending mode of the empty structure and the set (m2, f2, ζ2) represents the dynamic characteristics of the crowd. On these assumptions the governing equation of motion is: ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ = ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + − ⎥ + ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + − ⎥ + ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 0 0 0 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 1 p t x x k k k k k x x c c c c c x x m m & & && && (3) For the studies of this paper different structural systems are considered. They are all modelled as SDOF systems and the dynamic characteristics of the individual structures are listed in Table 1. 446
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