Identification of Structural Damage in Bridges Using High-Frequency Vibrational Responses

Table 2

First 35 natural frequencies for the undamaged and damaged structures.

Mode	Natural frequency			Difference in frequency with respect to undamaged structure
	(Hz)			Scenario 1		Scenario 2
	Undamaged structure	Scenario 1	Scenario 2	(Hz)	(%)	(Hz)	(%)
1	2.996	2.996	2.987	0.00	0.00	−0.01	−0.30
2	3.606	3.606	3.539	0.00	0.00	−0.07	−1.86
3	3.760	3.745	3.745	−0.01	−0.40	−0.01	−0.40
4	6.239	6.239	6.235	0.00	0.00	−0.01	−0.06
5	11.928	11.928	11.813	0.00	0.00	−0.12	−0.96
6	14.293	14.292	14.186	0.00	0.00	−0.11	−0.75
7	14.980	14.926	14.926	−0.05	−0.36	−0.05	−0.36
8	18.934	18.930	18.742	0.00	−0.02	−0.19	−1.01
9	26.643	26.643	26.281	0.00	0.00	−0.36	−1.36
10	31.648	31.648	31.380	0.00	0.00	−0.27	−0.85
11	33.561	33.548	33.540	−0.01	−0.04	−0.02	−0.06
12	36.746	36.720	36.530	−0.03	−0.07	−0.22	−0.59
13	46.699	46.699	46.208	0.00	0.00	−0.49	−1.05
14	53.023	52.955	52.584	−0.07	−0.13	−0.44	−0.83
15	54.670	54.660	54.112	−0.01	−0.02	−0.56	−1.02
16	59.232	59.035	58.996	−0.20	−0.33	−0.24	−0.40
17	70.642	70.640	70.375	0.00	0.00	−0.27	−0.38
18	74.713	74.608	74.365	−0.10	−0.14	−0.35	−0.47
19	81.175	81.150	80.450	−0.02	−0.03	−0.72	−0.89
20	90.023	89.795	89.653	−0.23	−0.25	−0.37	−0.41
21	92.564	92.424	91.303	−0.14	−0.15	−1.26	−1.36
22	97.630	97.597	97.067	−0.03	−0.03	−0.56	−0.58
23	108.580	108.386	108.211	−0.19	−0.18	−0.37	−0.34
24	114.964	114.942	114.221	−0.02	−0.02	−0.74	−0.65
25	124.176	124.142	123.241	−0.03	−0.03	−0.94	−0.75
26	133.840	133.800	132.782	−0.04	−0.03	−1.06	−0.79
27	140.715	140.578	140.040	−0.14	−0.10	−0.68	−0.48
28	150.078	150.064	149.134	−0.01	−0.01	−0.94	−0.63
29	157.242	157.093	156.630	−0.15	−0.09	−0.61	−0.39
30	164.279	164.279	163.880	0.00	0.00	−0.40	−0.24
31	165.131	165.090	164.276	−0.04	−0.02	−0.85	−0.52
32	173.047	173.043	172.217	0.00	0.00	−0.83	−0.48
33	196.072	195.862	194.716	−0.21	−0.11	−1.36	−0.69
34	199.703	199.646	198.997	−0.06	−0.03	−0.71	−0.35
35	211.179	210.875	209.775	−0.30	−0.14	−1.40	−0.66