Research Article
Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam
Table 4
Dimensionless frequency parameter
for the clamped supported Timoshenko beam.
| | Mode | Euler theory | | | Ferreira [10] | Lee and Schultz [12] | Proposed element |
| | 1 | 4.73004 | 4.7345 | 4.72998 | 4.72998 | | 2 | 7.85320 | 7.8736 | 7.85295 | 7.85296 | | 3 | 10.9956 | 11.0504 | 10.9950 | 10.9950 | | 4 | 14.1372 | 14.2526 | 14.1359 | 14.1360 | | 5 | 17.2788 | 17.4888 | 17.2766 | 17.2768 | | 6 | 20.4204 | 20.7670 | 20.4168 | 20.4174 | | 7 | 23.5619 | 24.0955 | 23.5567 | 23.5578 | | 8 | 26.7035 | 27.4833 | 26.6960 | 26.6980 | | 9 | 29.8451 | 30.9398 | 29.8348 | 29.8382 | | 10 | 32.9867 | 34.4748 | 32.9729 | 32.9786 |
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