Research Article
Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam
Table 5
Dimensionless frequency parameter
for the clamped supported Timoshenko beam.
| | Mode | Euler theory | | | Ferreira [10] | Lee and Schultz [12] | Proposed element |
| | 1 | 4.73004 | 4.7330 | 4.72840 | 4.72840 | | 2 | 7.85320 | 7.8675 | 7.84690 | 7.84692 | | 3 | 10.9956 | 11.0351 | 10.9800 | 10.9801 | | 4 | 14.1372 | 14.2218 | 14.1062 | 14.1064 | | 5 | 17.2788 | 17.4342 | 17.2246 | 17.2253 | | 6 | 20.4204 | 20.6783 | 20.3338 | 20.3355 | | 7 | 23.5619 | 23.9600 | 23.4325 | 23.4358 | | 8 | 26.7035 | 27.2857 | 26.5192 | 26.5253 | | 9 | 29.8451 | 30.6616 | 29.5926 | 29.6032 | | 10 | 32.9867 | 34.0944 | 32.6514 | 32.6687 |
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