Research Article
An Improved Analytical Method for Vibration Analysis of Variable Section Beam
Table 1
Comparison of results from ADTM and ADM in the uniform beam case.
| Frequency | Order of iteration | ADM | ADTM | FEM result | Theoretical result | (p = 2) | (p = 3) |
| ω1 | n = 1 | 79.0341 | 78.2747 | 78.1178 | 77.7096 | 78.0726 | n = 2 | 78.0743 | 78.0727 | 78.0726 | n = 3 | 78.0726 | 78.0726 | 78.0726 |
| Ω2 | n = 1 | 417.6492 | 454.8542 | 492.8109 | 487.1444 | 489.2727 | n = 2 | 456.9292 | 488.6935 | 489.2750 | n = 3 | 488.3615 | 489.2715 | 489.2727 |
| Ω3 | n = 1 | — | 1290.2621 | 1309.2891 | 1362.8536 | 1369.9775 | n = 2 | — | 1350.1889 | 1365.6756 | n = 3 | 1095.9032 | 1369.6495 | 1369.9640 |
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