Mathematical Problems in Engineering / 2011 / Article / Tab 8 / Research Article
A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam Table 8 Dimensionless frequencies for rotating beam with different inclination angle (
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𝛼
𝑘
𝜀
𝑐
m
a
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1
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−
5
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𝜀
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3
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𝑣
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/
𝐿
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1
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2
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𝐾
1
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𝐾
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𝐾
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4
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6
0 .000000 0 0 .351601 .220341 .616949 .120893 .199838 .298509 .010 14.8998 0 0 1.32581 .432338 .886010 .151855 .233376 .333736 .020 59.6058 0 0 2.52842 .766172 1.38410 .216189 .309541 .419056 0° .030 134.137 0 0 3.73648 1.11402 1.92511 .289167 .400408 .525942 .040 238.527 0 0 4.94495 1.46597 2.47903 .364653 .496007 .640880 .050 372.820 0 0 6.15267 1.81983 3.03912 .441165 .593428 .759068 .060 537.076 0 0 7.35907 2.17482 3.60301 .518237 .691707 .878747 .005 3.71469 .765147 5.97092 .741097 .289190 .695401 .129392 .208701 .307598 .010 14.8600 1.67568 7.33938 1.32573 .432307 .885745 .151766 .233190 .333432 5° .015 33.4431 2.57966 7.79173 1.92549 .595911 1.12500 .182037 .268266 .371976 .020 59.4713 3.46977 8.02050 2.52834 .766160 1.38402 .216153 .309441 .418839 .025 92.9513 4.34189 8.15957 3.13220 .939307 1.65211 .252155 .353965 .470793 .030 133.889 5.19316 8.25360 3.73641 1.11401 1.92507 .289150 .400356 .525817 .002 .542410 1.31449 16.2578 .436039 .231506 .625674 .121676 .200527 .299138 30° .004 2.15709 3.45499 31.0603 .628044 .264068 .655502 .124160 .202509 .300711 .006 4.84203 5.61881 37.4726 .851755 .312455 .712896 .129772 .207598 .305211 .008 8.61268 7.78502 40.6536 1.08530 .369468 .788930 .138176 .215896 .313013 .0005 .012524 .216407 3.11010 .352489 .220632 .617142 .120911 .199852 .298522 .0010 .050204 .860794 12.1582 .357434 .221288 .616084 .120749 .199640 .298279 .0015 .112068 1.89528 25.7173 .371925 .221920 .610342 .119952 .198654 .297181 90° .0020 .194123 3.21653 40.7205 .400095 .222722 .599365 .118425 .196788 .295121 .0025 .290775 4.68879 54.0272 .440751 .224723 .587411 .116669 .194633 .292734 .0030 .398355 6.21301 64.2905 .489485 .228876 .578807 .115177 .192740 .290595 .0035 .516056 7.74385 71.7152 .542488 .235452 .575106 .114128 .191302 .288900