184 M. Vanali et al. 22.3.2 Tests with Active People This subsection shows that the use of the model presented in Sect. 22.2.2 allows to improve the prediction of the structural response due to people moving. The tests were carried out by asking a given number of people to walk freely and all together on S1/S2. The acceleration responses of the structures were measured by means of accelerometers. The newly proposed approach is compared here to the experiments and to the use of the model of the empty structure directly excited by the AGRFs. The mentioned comparison is carried out in terms of root mean square (RMS) of the time-responses. Here, the resulting RMS values are related to the point of maximum response for both S1 and S2. The RMSs are calculated in the frequency range 0–15 Hz. The RMS values coming from the use of the models is represented as a mean value plus/minus twice the standard deviation. Indeed, since the AGRFs are sampled from a database of AGRFs (see Sect. 22.2.2), the result of a single simulation depends upon the AGRFs extracted from the database. Therefore, each case (i.e., a given number of people walking on either S1 or S2) was simulated 100 times to achieve a statistical reliability of the results by building of the resulting RMS values distributions (which were found to have a Gaussian trend). Figure 22.5a, b show the results related to the tests on S1 with three and nine people walking on the staircase, respectively. Figure 22.5c, d show the results related to the tests on S2 with five and ten people walking on the staircase, respectively. These plots demonstrate that the model proposed in Sect. 22.2.2 allows to satisfactorily estimate the experimental results. Furthermore, the use the FRF matrix GH as described in Sect. 22.2.2 allows to achieve results more accurate than the direct application of the AGRFs to the model of the empty structure (i.e., usingG). Fig. 22.5 Resulting RMS values: S1 with three people walking (a), S1 with nine people walking (b), S2 with five people walking (c) and S2 with ten people walking (d). The symbol GH on the vertical axis refers to the results related to model presented in Sect. 22.2.2, while the symbol G is related to the application of the AGRFs to the model of the empty structure. Plus symbols are related to experimental results, circle symbols are related to the mean value of the simulations results and square symbols are related to the mean value of the simulations results plus/minus twice the standard deviation of the simulation results
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