Research Article
Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam
Table 6
Dimensionless frequency parameter
for the clamped supported Timoshenko beam.
| | Mode | Euler theory | | | Ferreira [10] | Lee and Schultz [12] | Proposed element |
| | 1 | 4.73004 | 4.5835 | 4.57955 | 4.57962 | | 2 | 7.85320 | 7.3468 | 7.33122 | 7.33193 | | 3 | 10.9956 | 9.8924 | 9.85611 | 9.85918 | | 4 | 14.1372 | 12.2118 | 12.1454 | 12.1540 | | 5 | 17.2788 | 14.3386 | 14.2324 | 14.2513 | | 6 | 20.4204 | 16.3046 | 16.1487 | 16.1841 | | 7 | 23.5619 | 18.1375 | 17.9215 | 17.9807 | | 8 | 26.7035 | 19.8593 | 19.5723 | 19.6641 | | 9 | 29.8451 | 21.4875 | 21.1185 | 21.2523 | | 10 | 32.9867 | 23.0358 | 22.5735 | 22.7598 |
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