Research Article
Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section
Table 5
The first three order dimensionless natural frequencies of rotating tapered hollow beams for various ratio of inner radius to the root radius
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| 0 | | 4.0743 | 4.4869 | 5.4689 | 4.0021 | 4.3928 | 5.3165 | | 21.1137 | 22.8085 | 25.9958 | 19.1933 | 20.4539 | 22.8066 | | 55.0759 | 59.0308 | 65.6330 | 45.1361 | 47.2503 | 50.6619 |
| 5 | | 6.8283 | 7.0878 | 7.7613 | 6.6530 | 6.8756 | 7.4647 | | 24.2176 | 25.6314 | 28.3193 | 21.8856 | 22.8463 | 24.6981 | | 58.1504 | 61.7981 | 67.8694 | 47.5230 | 49.3294 | 52.2535 |
| 10 | | 11.5023 | 11.6837 | 12.1584 | 11.1927 | 11.3104 | 11.6424 | | 31.7436 | 32.6600 | 34.3608 | 28.4415 | 28.8297 | 29.6427 | | 66.4593 | 69.3894 | 74.1474 | 53.9527 | 55.0169 | 56.7149 |
| 15 | | 16.4109 | 16.5675 | 16.9725 | 15.9740 | 16.0415 | 16.2467 | | 41.2695 | 41.7660 | 42.5327 | 36.7455 | 36.5930 | 36.3560 | | 78.2143 | 80.3361 | 83.4935 | 62.9728 | 63.1570 | 63.3260 |
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