# Urgent, pls help : lateral vibration frequency of a simply supported (pinned-pinned) hollow circular beam,

• posted

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.