22 Numerical Model for Human Induced Vibrations 183 22.3 Experimental Tests This section describes the experimental campaign carried out to validate the model presented in Sect. 22.2. Two staircases were used as test-structures. One, named S1, is made up of steel and marble, its length is 12.03 m, its width is 1.80 m and the height is 5.22 m. The second one, named S2, is made up of steel and has marble sheets on the steps, its length is 13.30 m, its width is 1.80 m and the height is 5.60 m. The modal parameters of the empty structures were identified by means of experimental modal analysis [32] and the values of the eigenfrequencies and non-dimensional damping ratios are gathered in Tables 22.1 and 22.2. The modes taken into account are those in the frequency range 0–15 Hz, which is the frequency band where the humans are mostly able to influence the dynamics of the structures. 22.3.1 Tests with Passive People This subsection presents some results related to the validation of the model of Sect. 22.2.1, developed to model the influence of passive people on the dynamic behaviour of the hosting structure. Different people were asked to stay in given points of the staircases. Then, the structure was excited by using an electro-dynamic shaker laid down on the staircase and moving a mass. Therefore, the excitement was provided employing the inertial effect (more details about the way to excite the structure can be found in [6, 7]). Finally, the FRFs of the structure were estimated by measuring the structural response by means of accelerometers. Figure 22.4a, b show the FRFs (for some tests and points of the structure chosen as examples) in a given point of S1 and S2, respectively. The experimental results match the numerical expectations for both the structures, proving the reliability and accuracy of the proposed approach. Other tests gave a similar level of accordance between experiments and simulations. Therefore, they are not shown here for sake of conciseness. Table 22.1 Modal data identified experimentally for S1 in the frequency range 0–15 Hz (empty structure) Mode number !j/(2 ) [Hz] j [%] 1 7.84 0.33 2 8.89 0.43 Table 22.2 Modal data identified experimentally for S2 in the frequency range 0–15 Hz (empty structure) Mode number !j/(2 ) [Hz] j [%] 1 6.70 0.33 2 9.55 0.28 3 10.75 0.29 4 11.21 0.17 Fig. 22.4 FRF for S1 (a) andS2 (b)
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