Research Article
Free Vibration Analysis for Cracked FGM Beams by Means of a Continuous Beam Model
Table 2
The first three nondimensional natural frequencies of intact FGM beams.
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| Clamped-free | | | | | 0.2 | Yang and Chen [27] | 0.83 | 5.18 | 14.49 | Present | 0.8258 | 5.1752 | 14.4910 | 3D FEM | 0.8269 | 5.1270 | 14.1144 | 1.0 | Yang and Chen [27] | 0.88 | 5.51 | 15.42 | Present | 0.8790 | 5.5086 | 15.4243 | 3D FEM | 0.8799 | 5.4501 | 15.0078 | 5.0 | Yang and Chen [27] | 0.83 | 5.18 | 14.49 | Present | 0.8258 | 5.1752 | 14.4910 | 3D FEM | 0.8268 | 5.1270 | 14.1144 | Clamped-clamped | | | | | 0.2 | Yang and Chen [27] | 2.51 | 9.27 | 21.07 | Present | 2.3181 | 9.2724 | 20.8628 | 3D FEM | 2.3085 | 9.1219 | 20.0568 | 1.0 | Yang and Chen [27] | 2.47 | 9.87 | 22.21 | Present | 2.4674 | 9.8696 | 22.2066 | 3D FEM | 2.4579 | 9.7116 | 21.4361 | 5.0 | Yang and Chen [27] | 2.51 | 9.27 | 21.07 | Present | 2.3181 | 9.2724 | 20.8628 | 3D FEM | 2.3085 | 9.1219 | 20.0568 | Hinged-hinged | | | | | 0.2 | Yang and Chen [27] | 5.25 | 14.49 | 28.40 | Present | 5.2548 | 14.4852 | 28.3968 | 3D FEM | 5.2050 | 14.0623 | 26.8927 | 1.0 | Yang and Chen [27] | 5.59 | 15.42 | 30.23 | Present | 5.5933 | 15.4182 | 30.2258 | 3D FEM | 5.5319 | 14.9257 | 28.4977 | 5.0 | Yang and Chen [27] | 5.25 | 14.49 | 28.40 | Present | 5.2548 | 14.4852 | 28.3968 | 3D FEM | 5.2050 | 14.0623 | 26.8927 |
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