Dear all,
I really need the help from you experts.
I am trying to use ANSYS to find out the LATERAL vibration natural frequncies of a simply supported (at both ends) beam. The cross section of the beam is a hollow circular with inner radius ri = 3.9525", outer radius = 4.2025. The length of the beam is L=73.775". Young's module is E=30E6 psi, density is p=0.298 lbm/in^3.
Below is my approach: I used element 25 to model this axissymmetry structure. In the thickness direction, I have 4 divisions, which I think is good enough. Then I fully constrained two center nodes at two ends of the beam to model the pinnned-pinned b.c.'s. Then I run the *.db file by following codes:
/solu allse,all antype,modal, mode,1,1, modopt,lanb,10,0,10000 solve
I got the following freq's (in Hz):
823.57 (1st mode).
1647.33 (2nd mode).
2471.50 ...
3296.28
4121.87
4948.47
5776.28
6605.51
7436.36
8269.03
The modal shapes look ok. They are in the radial-axial plan, having 0,
1, 2..., and so on, nodal points. But the above freq's do not match those given by text book, which is: fi=Ci*sqrt(E*I/(p*A*L^4)), where Ci=9.87,39.5, and 88.9 for the first three modes. So, the freq. should be:
168.63, 674.53, and 1518.0 hZ, and so on.
Can somebody tell me where I did something wrong, please help!
Thanks a lot in advance.
wangming Lu GE Energy
300 Garlington Rd. Greenville, SC 29615 Tel: 864-255-3378