Research Article
An Improved Analytical Method for Vibration Analysis of Variable Section Beam
Table 3
Comparison of results from various methods in four cases.
| | Beam model | Frequency | FEM | ADTM
(n = 10, p = 3, k1 = 10, k2 = 10, k3 = 11) | ADM (n = 26, k = 10) | Semianalytical method (p = 8) | | Result (rad/s) | Result (rad/s) | Error (‰) | Result (rad/s) | Error (‰) | Result (rad/s) | Error (‰) |
| | Trapezoidal beam | ω1 | 102.1261 | 101.8169 | 3.0 | 101.8159 | 3.0 | 101.3213 | 7.9 | | ω2 | 535.4677 | 533.3845 | 3.9 | 533.3869 | 3.9 | 530.4472 | 9.4 | | ω3 | 1423.3859 | 1415.5921 | 5.4 | 1415.5946 | 5.5 | 1407.6242 | 11.1 |
| | Trapezoidal convex beam | ω1 | 99.5983 | 99.2801 | 3.1 | 99.2813 | 3.1 | 98.7987 | 8.1 | | ω2 | 536.2030 | 533.8025 | 4.5 | 533.7847 | 4.5 | 530.2409 | 11.1 | | ω3 | 1428.8301 | 1420.9610 | 5.5 | 1421.9121 | 4.8 | 1410.5328 | 12.8 |
| | Concave beam | ω1 | 73.9735 | 74.2340 | 3.5 | — | — | 74.5634 | 7.9 | | ω2 | 499.8834 | 497.9771 | 3.8 | — | — | 496.4176 | 6.9 | | ω3 | 1385.9541 | 1378.6030 | 5.3 | — | — | 1374.8716 | 7.9 |
|
|
