172 A.S. Mohammed and A. Pavic Fig. 21.3 Amplitude-dependent values of (a) damping ratio and (b) fundamental frequency of the test structure 21.3.2 Walking Tests Walking tests were carried out individually by four male test subjects. Their weight range between 820 and 900 N and they were denoted as (TS1, TS2, TS3 and TS4). To take into account the intra-subject variability, each TS performed six walking tests at two pacing frequencies: 1.90 Hz and 2.05 Hz (12 walking tests in total). The second harmonic of the former pacing frequency excites the first bending mode of the footbridge and produces a resonant response. The later pacing frequency is chosen to obtain a non-resonant response. All walking tests were controlled by a metronome and each TS had to wait for about 10 s (at the location of one of the supports) between every two successive tests to allow for the vibration decay. The vibration response for each case was measured at the anti-node of the first vibration mode (mid-span of the footbridge). 21.3.3 Simulation of Vibration Responses The identified dynamic properties of the first bending mode (Sect. 21.3.1) were utilised in the simulations of vibration responses. A MATLAB script was developed to take into account the amplitude-dependent damping ratio and fundamental frequency. The values of these parameters were updated after each cycle of the simulated vibration responses. The simulations carried out in this study can be classified into two groups: • Non-interactive models, for which HSI is neglected and only the walking force is applied on the oscillator of the vibration mode, and • Interactive models, which include the HSI of walking people (as discussed in Sect. 21.2). For each group, two types of walking forces are utilised: • Measured walking forces for corresponding test subjects, and • Deterministic walking force function based on Fourier series representation which can be mathematically described in Eq. (21.1): F.t/ DW 1C N XnD1 ˛nsin 2n fp C¿n ; (21.1)
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