23 Dynamic Testing on the New Ticino Bridge of the A4 Highway 193 Fig. 23.7 TO-MI way: PSD, the arrows indicate modes of vibration of lower amplitude of which is difficult to identify reliably the mode shape Table 23.2 Modal parameters of TO-MI bridge Mode Frequency (Hz) Damping ratio (%) 1 1.27 0.52 2 1.36 0.51 3 1.51 0.52 4 1.71 0.45 5 1.77 0.71 6 1.82 0.43 7 1.92 0.42 8-1 2.07 0.49 8-2 2.08 0.53 9 2.20 0.47 10 2.24 0.38 23.4.3 Test Results and Model Tuning Activity This good agreement came after some model tuning was performed. In this case, the most important modelling assumption to refine was the behavior of the pendula, because all the rest of the geometry, masses and boundary conditions had been accurately reproduced in the FE model. On the other hand, as discussed before, the real behavior of the pendula in their elastic branch needed to be reproduced in order to be compared with the mode shapes identified at very low levels of vibration. At the beginning of the modelling process, the pendula were considered as fixed restrains to simulate the stiff frictional branch. This assumption caused some modes to disappear and limited the translational vibrations of the bridge along single spans, a fact that was considered non realistic. To overcome this excessive simplification, the correct force-displacement law was introduced, but still the pendulum at one single support were modelled as ‘lumped’ in one single node of the mesh. This option turned out to be ineffective because in this case in the FE model some additional irregular modes appeared, which were not representative of the physical behavior of a symmetric bridge having regular spans. Finally, after a few attempts, the number of nine springs for each isolator, each of them having a stiffness of 1/9th of the total and located at nine adjacent nodes of the mesh, gave “smoother” and more realistic numerical results for the mode shapes, as shown in the next section. In fact, these modeling assumptions reflected the behavior of the pendulum, whose physical dimension is much larger than one single node of the mesh chosen for the bridge deck.
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