Dynamics of Civil Structures, Volume 2

13 Mass Scaling of Mode Shapes Based on the Effect of Traffic on Bridges: A Numerical Study 105 The MSF values indicate that in each traffic scenario, average error is in an acceptable range below 15% and the maximum error value is as high as the conventional mass change method for specific frequency shifts [9]. Moreover, both maximum and average error percentages increase with the mode shape number. Therefore, if desired traffic conditions are satisfied and distribution of traffic headway times are known, with the help of repetitive tests, the scale factors can be calculated with promising accuracy. 13.4 Conclusion In this article, traffic induced mass change is considered to provide the required mass modification. The average mass loading of traffic is calculated for a range of near congestion traffic and a polynomial surface is fitted through the values to calculate the mass change matrix needed in the scaling factor equations. Therefore, in case of traffic conditions which satisfy the lognormal distribution of headways, the mass change matrix can be constructed using the proposed procedure. A finiteelement model of a bridge is considered and the method is evaluated for the first three modes of vibration of the structure using iterative tests and four real traffic conditions. The results indicate that for each traffic scenario, scale factors can be calculated with promising accuracy and the coefficients of variations are lower than 5%. Furthermore, the mean value of MSF errors are lower than 15% and the maximum MSF errors are as low as the conventional mass change methods. Therefore, it can be concluded that in cases of near congestion traffic streams which can be assumed stationary and are able to produce sufficient frequency shifts, the method can be used to derive the scale factors of the mode shapes. However, there are several assumptions made to simplify the problem in this study which are not present in the real situations. Nevertheless, the method can be further developed to account for different uncertainties and more robust modal identification approaches. References 1. Magalhães, F., Cunha, A.: Explaining operational modal analysis with data from an arch bridge. Mech. Syst. Signal Process. 25(5), 1431–1450 (2011) 2. López Aenlle, M., Brincker, R., Fernández Canteli, A.C.: Some methods to determine scaled mode shapes in natural input modal analysis. In: Proceedings of the IMAC-XXIII: Conference & Exposition on Structural Dynamics – Structural Health Monitoring (2005) 3. López-Aenlle, M., Brincker, R., Pelayo, F., Canteli, A.F.: On exact and approximated formulations for scaling-mode shapes in operational modal analysis by mass and stiffness change. J. Sound Vib. 331(3), 622–637 (2012) 4. Parloo, E., Verboven, P., Guillaume, P., Van Overmeire, M.: Sensitivity-based operational mode shape normalization. Mech. Syst. Signal Process. 16(5), 757–767 (2002) 5. Parloo, E., Cauberghe, B., Benedettini, F., Alaggio, R., Guillaume, P.: Sensitivity-based operational mode shape normalisation: application to a bridge. Mech. Syst. Signal Process. 19(1), 43–55 (2005) 6. Brincker, R., Andersen, P.: A way of getting scaled mode shapes in output only modal testing. In: Proceedings of the IMAC-XXI: International Modal Analysis Conference, Kissimmee, FL, p. 141 (2003) 7. López Aenlle, M., Brincker, R., Fernández Canteli, A.C., Villa García, L.M.: Scaling factor estimation by the mass change method. In: Proceedings of the International Operational Modal Analysis Conferencee (IOMAC), Copenhagen, Denmark (2005) 8. López Aenlle, M., Fernández Fernández, P., Brincker, R., Fernández Canteli, A.C.: Scaling factor estimation using an optimized mass change strategy, part 1: theory. 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