170 A.S. Mohammed and A. Pavic 21.2 Human-Structure Interaction Models of Walking Humans The existence of walking people is proven to have an effect on the dynamic behaviour of their accommodating structure. This effect can be mainly observed as an increased modal damping and a change in natural frequency due to the coupling between the walking people and supporting structure during walking [1, 5, 12]. HSI models of walking humans can generally be divided into three groups according to their approaches: mass-springdamper (MSD) models, inverted-pendulum models and more complex models of the human body. This paper considers only the first group, as it is the most widely used and user-friendly approach in the vibration serviceability community. It comprises either a single or multiple MSDs attached to the supporting structure, replicating the dynamic behaviour of a walking human, as shown in Fig. 21.1. In this study, the performance of six experimentally-developed MSD models of a single person walking [6–11] were compared. These models represent nominally identical human walking and the only difference between them is the parameters of the mass, stiffness and damping. Table 21.1 presents MSD parameters of eight experimentally-developed models of HSI of walking humans available in the literature. The model presented by Lou et al. [13] is excluded from the comparison, as the suggested range of natural frequency of the walking human is considerably below the range reported of other models. The model presented by Silva [14] is also excluded from the comparison. It was originally developed for crowds of walking people based a model of a single walking human [8]. These two models [8, 14] have relatively close MSD parameters so the model presented in [14] is excluded. Fig. 21.1 MSD representation of a walking human on a simply supported footbridge beam Table 21.1 Experimentally developed MSD parameters for walking human model available in the literature Damping No. Study Natural frequency (f ) (Hz) Mass (m) (kg) Stiffness (k) (N/m) Damping coefficient (c) (Ns/m) Damping ratio (%) 1 Jiménez-Alonso and Sáez [6] 2.75 84% of body mass ( M) – – 47 2 Lou et al. [13] 1.25–1.60 100% of body mass ( M) – – 37–50 3 Shahabpoor et al. [7] 2.75–3.0 100% of body mass ( M) – – 27.5–30 4 Silva and Pimentel [8] – 97.082C0.275 M 37.518 fp 30351.744 50.26 cC0.035 c2 29.041 m0.883 – 5 Silva et al. [14] – 97.082C0.275 M 37.518 fp 5758.441C 11.103 c 107.455C 16.208 m – 6 Toso et al. [9] – a b c – 7 Van Nimmen et al. [10] 2.5–4.0 95% of body mass – – 20–40 8 Zhang et al. [11] 1.85 100% of body mass – – 30 amD 231:34C3:69 MC145:06 f p 1:97 M fp C0:005 M2 15:25 f 2 p bk D75601:45 1295:32 M 33786:75f p C506:44 M fp C3:59 M2 C539:39 f 2 p ccD 1115.69C92.56 M 108.94 mC2.91 Mm 1.33 M2 1.30 m2
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