Mathematical Problems in Engineering / 2011 / Article / Tab 7 / 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 7 Dimensionless frequencies for rotating beam with different inclination angle (
𝜂
=
1
0
0
,
𝑅
=
1
).
𝛼
𝑘
𝜀
𝑐
m
a
x
(
1
0
−
4
)
𝜀
𝑏
m
a
x
(
1
0
−
3
)
𝑣
t
i
p
/
𝐿
𝑇
(
1
0
−
3
)
𝐾
1
(
1
0
−
1
)
𝐾
2
𝐾
3
𝐾
4
(a )
𝐾
5
𝐾
6
0 .000000 0 0 .351520 .219989 .614602 1.20047 1.57086 1.97619 .010 1.48998 0 0 .375696 .223163 .617963 1.20402 1.57096 1.97983 .020 5.96058 0 0 .439855 .232418 .627926 1.21458 1.57124 1.99072 0° .030 13.4137 0 0 .528670 .247050 .644140 1.23194 1.57172 2.00872 .040 23.8527 0 0 .630838 .266138 .666082 1.25578 1.57240 2.03361 .050 37.2820 0 0 .740095 .288755 .693127 1.28568 1.57327 2.06512 .060 53.7076 0 0 .853195 .314093 .724614 1.32116 1.57433 2.10288 .005 .371547 .184139 2.62891 .357708 .220785 .615441 1.20136 1.57089 1.97710 .010 1.48624 .688585 9.52242 .375636 .223154 .617940 1.20397 1.57105 1.97985 5° .015 3.34416 1.40679 18.5127 .403666 .227045 .622062 1.20826 1.57140 1.98446 .020 5.94540 2.23838 27.6550 .439745 .232381 .627773 1.21419 1.57195 1.99093 .025 9.29010 3.11970 35.8627 .481914 .239066 .635040 1.22176 1.57261 1.99922 .030 13.3786 4.01960 42.7784 .528564 .246988 .643816 1.23096 1.57329 2.00929 .002 .054294 .172596 2.48732 .352403 .220106 .614725 1.20060 1.57087 1.97632 .004 .217197 .683326 9.79956 .355052 .220456 .615081 1.20096 1.57097 1.97675 30° .006 .488756 1.51188 21.5060 .359467 .221033 .615636 1.20145 1.57136 1.97753 .008 .869003 2.62713 36.9471 .365637 .221832 .616344 1.20197 1.57227 1.97873 .010 1.35790 3.99065 55.3127 .373528 .222846 .617163 1.20241 1.57395 1.98043 .002 .020005 .346383 4.99669 .351634 .220038 .614651 1.20052 1.57089 1.97625 .004 .080103 1.38532 19.9425 .352038 .220178 .614748 1.20053 1.57127 1.97654 90° .006 .180478 3.11497 44.6708 .352915 .220392 .614736 1.20014 1.57288 1.97728 .008 .321226 5.52831 78.7975 .354553 .220651 .614373 1.19878 1.57704 1.97891 .010 .502064 8.60794 121.586 .357326 .220924 .613368 1.19581 1.58523 1.98201