13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Table 1. Comparison of natural frequencies computed by analytical method and finite-element method for Timoshenko portal frame with crack located in left vertical segment. Natural frequencies (Hz) Analytical method Finite element method % Difference End cond Crack loc. δ a/h ω1 ω2 ω3 ω1 ω2 ω3 ω1 ω2 ω3 nocrack 278.97 1247.63 1874.68 284.72 1253.30 1915.70 2.02 0.45 2.14 0.2 273.59 1246.07 1874.27 278.67 1250.30 1914.10 1.82 0.34 2.08 0.4 259.76 1242.22 1873.25 263.04 1241.50 1909.00 1.25 -0.06 1.87 0.2 0.6 242.61 1237.76 1872.06 239.40 1226.50 1898.60 -1.34 -0.92 1.40 0.2 277.82 1246.41 1870.52 283.40 1252.70 1912.40 1.97 0.50 2.19 0.4 274.53 1242.68 1855.99 279.40 1251.40 1901.20 1.74 0.70 2.38 0.4 0.6 269.52 1236.45 1825.18 271.45 1249.70 1851.60 0.71 1.06 1.43 0.2 278.39 1238.80 1866.35 284.15 1245.80 1908.50 2.03 0.56 2.21 0.4 276.67 1212.19 1842.10 282.47 1225.10 1888.50 2.05 1.05 2.46 F-H 0.7 0.6 273.87 1169.33 1806.42 279.38 1186.20 1846.20 1.97 1.42 2.15 nocrack 171.26 1127.17 1699.66 175.89 1127.60 1725.90 2.63 0.04 1.52 0.2 171.05 1121.54 1684.13 175.73 1123.00 1707.30 2.66 0.13 1.36 0.4 170.33 1100.86 1631.91 175.24 1106.70 1635.10 2.80 0.53 0.20 0.2 0.6 168.74 1049.62 1536.78 174.02 1044.30 1435.10 3.03 -0.51 -7.09 0.2 170.47 1112.51 1669.77 175.15 1114.30 1691.40 2.67 0.16 1.28 0.4 167.87 1062.04 1590.26 172.84 1068.80 1590.50 2.88 0.63 0.02 0.4 0.6 162.52 963.96 1501.23167.14 944.69 1438.70 2.76 -2.04-4.35 0.2 169.22 1116.83 1695.43 173.83 1118.50 1721.50 2.65 0.15 1.51 0.4 162.97 1086.81 1684.06 167.78 1093.50 1707.90 2.87 0.61 1.40 H-H 0.7 0.6 152.36 1041.43 1669.02 155.49 1047.50 1680.50 2.01 0.58 0.68 nocrack 371.92 1412.93 2299.39 379.70 1426.70 2333.60 2.05 0.97 1.47 0.2 367.23 1411.38 2298.55 374.29 1423.10 2332.90 1.89 0.82 1.47 0.4 355.35 1407.55 2296.43 360.43 1412.50 2329.90 1.41 0.35 1.44 0.2 0.6 340.98 1403.10 2293.85 339.92 1393.40 2323.80 -0.31 -0.70 1.29 0.2 371.14 1410.18 2275.30 378.75 1425.20 2306.00 2.01 1.05 1.33 0.4 368.89 1401.69 2193.73 375.81 1421.60 2197.10 1.84 1.40 0.15 0.4 0.6 365.49 1387.23 2076.01 369.81 1415.80 1963.20 1.17 2.02 -5.75 0.2 371.08 1399.78 2285.05 378.86 1415.70 2318.50 2.05 1.12 1.44 0.4 368.56 1361.07 2243.52 376.45 1386.10 2286.90 2.10 1.81 1.90 F-F 0.7 0.6 364.46 1301.56 2186.91 372.01 1331.50 2155.50 2.03 2.25 -1.46 Note: F-H - Fixed-hinged, H-H – Hinged-hinged and F-F – fixed-fixed end conditions.
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