GNGTS 2014 - Atti del 33° Convegno Nazionale

322 GNGTS 2014 S essione 2.3 Interpretation of dynamic test results. Careful analysis of experimental FRF curves suggested the use of responses to excitation along the transverse (T), longitudinal (L) or vertical (V) directions for the reconstruction of the dynamic properties and vibrating modes with prevailing amplitudes along the T, L or V-directions respectively. The experimental FRF curves resulted almost regular in the low frequency range (1-6 Hz). Some difficulties have been encountered in the analysis of FRFs at high frequencies (12-15 Hz), due to the presence of more pronounced irregularities and low amplitude measurements. Fig. 2b shows a comparison between some measured and synthesized point inheritance functions of the bridge. Vibration modes generally resulted in resonance frequencies well separated, with the exception of the pairs of modes (2, 3) and (6, 7). Modes 2 and 3 were easily identified, since their modal shape corresponds to vibrations with prevailing amplitudes in the horizontal plane and along the vertical direction, respectively. A different situation was encountered for Modes 6-7, since both of them are primarily vertical modes. In this case, it is found convenient to analyze the FRFs obtained as the half-difference and the half-sum of the FRFs measured in points belonging to the same cross-section of the deck. In general terms, the half-sum allows in fact to remove torsional contributions in the measured deformations, thus to take into account the bending vibrations only. Conversely, the FRF obtained as half-difference emphasizes the torsional component of the modal deformation (Fig. 2c). This method allowed to reconstruct separately Modes 6 and 7, under the assumption that amplitudes of oscillation of the points belonging to the transverse cross-section of the deck are equal (in absolute value). Tab. 1 summarizes the results of the Experimental Modal Analysis (EMA). Natural frequencies are the average values obtained from the analysis of FRF curves. As shown, deviations from the average values can be considered negligible for modes at low frequency, while differences generally increase with the mode order. The estimation of the damping ratios is equally good, although differences are important for some higher order modes. Based on damping ratios collected in Tab. 1, it can be observed that bending and torsional modes of the deck generally have lower damping terms (≈ 0.7-1.8%), compared to typically high damping values of almost- rigid body motions (≈ 2.9-4.3%), in which the energy dissipation arising from the elastomeric bearings can be appreciated. Tab. 1 - Experimental Modal Analysis results. Mean value of natural frequency f and damping ratio ξ , with corresponding maximum deviations. B= Bending; T= Torsional; RB= almost rigid-body motions. r [-] Description [-] f [Hz] ξ [%] 1 1st B 2.022 ± 0.001 0.88 ± 0.03 2 RB Transverse 3.053 ± 0.003 2.88 ± 0.05 3 2nd B 3.180 ± 0.002 0.89 ± 0.05 4 RB Longitudinal 3.605 ± 0.002 4.33 ± 0.07 5 RB Torsional 4.831 ± 0.011 3.93 ± 0.13 6 1st T 6.887 ± 0.046 Not available 7 3rd B 6.924 ± 0.015 1.15 ± 0.20 8 2nd T 7.995 ± 0.005 0.88 ± 0.10 9 4th B 9.107 ± 0.020 1.78 ± 0.44 10 Coupled B-T 12.910 ± 0.025 1.66 ± 0.20 11 Coupled B-T 14.228 ± 0.081 0.66 ± 0.12 12 Coupled B-T 14.433 ± 0.100 0.77 ± 0.27