From: Flapwise bending vibration analysis of functionally graded rotating double-tapered beams
τ h | τ b | 0.2 | 0.4 | 0.6 | 0.8 |
---|---|---|---|---|---|
0.0 | |||||
(a) Fundamental frequency | |||||
0.0 | 3.15601 | 3.76285 | 4.09697 | 4.58531 | 5.39758 |
3.51602a | 3.76286a | 4.09698a | 4.58531a | 5.39759a | |
0.2 | 3.60827 | 3.85511 | 4.18932 | 4.67815 | 5.49265 |
3.60828a | 3.85512a | 4.18932a | 4.67816a | 5.49266a | |
0.4 | 3.73707 | 3.98419 | 4.31877 | 4.80842 | 5.62551 |
3.73708a | 3.98419a | 4.31878a | 4.80842a | 5.62552a | |
0.6 | 3.93427 | 4.18234 | 4.51799 | 5.00903 | 5.82882 |
3.93428a | 4.18235a | 4.51799a | 5.00903a | 5.82882a | |
0.8 | 4.29250 | 4.54369 | 4.88244 | 5.37615 | 6.19641 |
4.29249a | 4.54368a | 4.88244a | 5.37614a | 6.19639a | |
(b) Second natural frequency | |||||
0.0 | 22.0344 | 22.5018 | 23.1186 | 24.0210 | 25.6558 |
22.0345a | 22.5018a | 23.1186a | 24.0211a | 25.6558a | |
0.2 | 20.6210 | 21.0567 | 21.6327 | 22.4774 | 24.0153 |
20.6210a | 21.0567a | 21.6327a | 22.4774a | 24.0153a | |
0.4 | 19.1138 | 19.5166 | 20.0500 | 20.8343 | 22.2710 |
19.1138a | 19.5166a | 38.4920a,b | 20.8343a | 22.2710a | |
0.6 | 17.4879 | 17.8557 | 18.3441 | 19.0649 | 20.3953 |
17.4879a | 17.8557a | 18.3441a | 19.0649a | 20.3952a | |
0.8 | 15.7473 | 16.0731 | 16.5132 | 17.1668 | 18.3871 |
15.7427a | 16.0725a | 16.5123a | 17.1657a | 18.3855a | |
(c) Third natural frequency | |||||
0.0 | 61.6972 | 62.1525 | 62.7763 | 63.7515 | 65.7470 |
61.6972a | 62.1525a | 62.7763a | 63.7515a | 65.7470a | |
0.2 | 56.1923 | 56.6304 | 57.2258 | 58.1467 | 60.0096 |
56.1923a | 56.6303a | 57.2257a | 58.1466a | 60.0094a | |
0.4 | 50.3537 | 50.7715 | 51.3348 | 52.1965 | 53.9177 |
50.3537a | 50.7714a | 51.3346a | 52.1963a | 53.9173a | |
0.6 | 44.0252 | 44.4180 | 44.9437 | 45.7391 | 47.3066 |
44.0248a | 44.4175a | 44.9432a | 45.7384a | 47.3051a | |
0.8 | 36.8955 | 37.2558 | 37.7358 | 38.4555 | 39.8568 |
36.8846a | 37.2439a | 37.7223a | 38.4392a | 39.8336a |