Mathematical Problems in Engineering / 2011 / Article / Tab 5 / 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 5 Dimensionless frequencies for rotating beam with different inclination angle (
𝜂
=
3
9
,
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
𝐾
5
𝐾
6
(a )0 0 0 0 .900168 .559057 1.54325 1.57086 (a ) 2.96396 4.71413 .010 1.48999 0 0 .909817 .560283 1.54452 1.57097 (a ) 2.96528 4.71415 .020 5.96060 0 0 .938126 .563945 1.54830 1.57130 (a ) 2.96926 4.71421 0° .030 13.4138 0 0 .983359 .569996 1.55455 1.57190 (a ) 2.97586 4.71432 .040 23.8528 0 0 1.04313 .578359 1.56302 1.57296 (a ) 2.98509 4.71449 .050 37.2822 0 0 1.11488 .588935 1.57113 1.57704 (a ) 2.99691 4.71472 .060 53.7078 0 0 1.19620 .601604 1.57358 (a ) 1.58936 3.01129 4.71502 .005 .371545 .073310 .412011 .902582 .559363 1.54357 1.57089 (a ) 2.96429 4.71414 .010 1.48623 .289977 1.62160 .909786 .560280 1.54449 1.57100 (a ) 2.96528 4.71415 5° .015 3.34417 .640707 3.55360 .921661 .561805 1.54595 1.57126 (a ) 2.96693 4.71416 .020 5.94559 1.11150 6.09535 .938019 .563932 1.54784 1.57177 (a ) 2.96925 4.71416 .025 9.29075 1.68547 9.11211 .958617 .566654 1.55003 1.57268 (a ) 2.97222 4.71415 .030 13.3800 2.34473 12.4630 .983170 .569962 1.55233 1.57416 (a ) 2.97585 4.71413 .002 .054292 .067510 .379956 .900509 .559102 1.54330 1.57087 (a ) 2.96401 4.71413 .004 .217174 .269614 1.51631 .901534 .559237 1.54341 1.57090 (a ) 2.96415 4.71413 30° .006 .488657 .605041 3.39858 .903243 .559461 1.54355 1.57103 (a ) 2.96440 4.71412 .008 .868763 1.07170 6.00953 .905635 .559775 1.54362 1.57132 (a ) 2.96474 4.71409 .010 1.35752 1.66673 9.32547 .908710 .560177 1.54351 1.57191 (a ) 2.96518 4.71403 .002 .019999 .135091 .760426 .900208 .559076 1.54327 1.57087 (a ) 2.96398 4.71413 .004 .080009 .540362 3.04080 .900333 .559132 1.54324 1.57098 (a ) 2.96404 4.71412 90° .006 .180072 1.21579 6.83830 .900554 .559224 1.54295 1.57140 (a ) 2.96415 4.71407 .008 .320253 2.16132 12.1478 .900889 .559349 1.54211 1.57246 (a ) 2.96431 4.71394 .010 .500631 3.37678 18.9613 .901363 .559506 1.54041 1.57447 (a ) 2.96451 4.71365
