Research Article
Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam
Table 1
Dimensionless frequency parameter
for the simply supported Timoshenko beam.
| | Mode | Euler theory | | | Ferreira [10] | Lee and Schultz [12] | Proposed element |
| | 1 | 3.14159 | 3.1428 | 3.14158 | 3.14158 | | 2 | 6.28319 | 6.2928 | 6.28310 | 6.28310 | | 3 | 9.42478 | 9.4573 | 9.42449 | 9.42450 | | 4 | 12.5664 | 12.6437 | 12.5657 | 12.5657 | | 5 | 15.7080 | 15.8596 | 15.7066 | 15.7068 | | 6 | 18.8496 | 19.1127 | 18.8473 | 18.8476 | | 7 | 21.9911 | 22.4113 | 21.9875 | 21.9883 | | 8 | 25.1327 | 25.7638 | 25.1273 | 25.1288 | | 9 | 28.2743 | 29.1793 | 28.2666 | 28.2692 | | 10 | 31.4159 | 32.6672 | 31.4053 | 31.4098 |
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