13 Mass Scaling of Mode Shapes Based on the Effect of Traffic on Bridges: A Numerical Study 103 Table 13.4 Statistical parameters of scale factors regarding each traffic case Case no. Mode shape no. Mean value of frequency !1 (rad/s) Mean frequency shift (%) Mean value of normalized˛ Coefficient of variation (CV) Case 1 1 12.57 2 0.974 0.052 2 50.35 2 0.951 0.044 3 113.38 2 0.939 0.047 Case 2 1 12.57 2 0.977 0.044 2 50.36 2 0.947 0.051 3 113.37 2 0.940 0.047 Case 3 1 12.57 2 0.979 0.043 2 50.36 2 0.948 0.049 3 113.38 2 0.937 0.052 Case 4 1 12.57 2 0.976 0.041 2 50.37 2 0.945 0.047 3 113.40 2 0.935 0.046 Node number 1 2 3 4 5 6 7 8 9 Normalized mode shape 0 0.05 0.1 0.15 0.2 0.25 (a) (b) (c) OMA Re-scaled OMA Correctly scaled Node number 1 2 3 4 5 6 7 8 9 Normalized mode shape −0.2 −0.1 0 0.1 0.2 OMA Re-scaled OMA Correctly scaled Node number 1 2 3 4 5 6 7 8 9 Normalized mode shape −0.2 −0.1 0 0.1 0.2 OMA Re-scaled OMA Correctly scaled Fig. 13.9 Comparison of unscaled OMA mode shapes and re-scaled modes with correctly scaled mode shapes from FEM model for a typical simulation of the first traffic case. (a)Mode 1. (b)Mode 2. (c)Mode 3 Modal Scaling Factor (MSF) error is then calculated using Eq. (13.23) between the scaled mode shapes and FEM mode shapes [9]. Maximum and average error values are shown in Fig. 13.11 for each traffic case. Errori D100 ˇ ˇ ˇ ˇ ˇ 1 ˛2 i :§0 T i :§0i ®T i :®i ˇ ˇ ˇ ˇ ˇ (13.23)
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