Research Article
Application of Adomian Modified Decomposition Method to Free Vibration Analysis of Rotating Beams
Table 1
The first five dimensionless natural frequencies
(
n) for a clamped-free beam with different dimensionless rotating speeds
U and offset lengths
R.
| R | U | Methods | Mode index n | 1 | 2 | 3 | 4 | 5 |
| 0 | 0 | Present | 3.516015 | 22.034492 | 61.697214 | 120.901916 | 199.859530 | [4] | 3.5160 | 22.0345 | 61.6972 | 120.902 | 199.860 | 1 | Present | 3.681647 | 22.181011 | 61.841763 | 121.050922 | 200.011574 | [3] | 3.6816 | 22.1810 | 61.8418 | — | — | 2 | Present | 4.137320 | 22.614922 | 62.273184 | 121.496695 | 200.466923 | [3] | 4.1373 | 22.6149 | 62.2732 | — | — | 3 | Present | 4.797279 | 23.320264 | 62.984967 | 122.235547 | 201.223245 | [3] | 4.7973 | 23.3203 | 62.9850 | — | — | 12 | Present | 13.170150 | 37.603112 | 79.614478 | 140.534354 | 220.536322 | [4] | 13.1702 | 37.6031 | 79.6145 | 140.534 | 220.536 |
| 1 | 1 | Present | 3.888824 | 22.375014 | 62.043053 | 121.263205 | 200.230870 | [3] | 3.8888 | 22.3750 | 62.0431 | — | — | 2 | Present | 4.833689 | 23.366042 | 63.067548 | 122.339546 | 201.340072 | [3] | 4.8337 | 23.3660 | 63.0675 | — | — | 4 | Present | 7.475048 | 26.957262 | 66.986772 | 126.537325 | 205.706683 | [3] | 7.475 | 26.9573 | 66.9868 | — | — | 8 | Present | 13.507389 | 37.953793 | 80.529532 | 141.877971 | 222.165291 | [3] | 13.5074 | 37.9538 | 80.5295 | — | — | 15 | Present | 24.409202 | 61.437052 | 113.488866 | 182.695785 | 268.831067 | [1] | 24.4092
| 61.4371 | 113.4889 | — | — |
| 2 | 1 | Present | 4.085335 | 22.567257 | 62.243575 | 121.475038 | 200.449876 | [3] | 4.0853 | 22.5673 | 62.2436 | — | — | 2 | Present | 5.439949 | 24.092373 | 63.850233 | 123.175402 | 202.208659 | [3] | 5.4399 | 24.0924 | 63.8502 | — | — | 4 | Present | 8.966379 | 29.380507 | 69.852259 | 129.712377 | 209.068207 | [3] | 8.9664 | 29.3805 | 69.8523 | — | — |
| 3 | 1 | Present | 4.272659 | 22.757784 | 62.443336 | 121.686425 | 200.668594 | [3] | 4.2727 | 22.7578 | 62.4433 | — | — | 2 | Present | 5.983713 | 24.796124 | 64.621696 | 124.004411 | 203.072744 | [3] | 5.9837 | 24.7961 | 64.6217 | — | — | 4 | Present | 10.236798 | 31.604901 | 72.583135 | 132.794372 | 212.364626 | [1] | 10.2368 | 31.6049 | 72.5831 | — | — |
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