Ansys Modal analysis on simple cantilever beam

[vonMech]

Hi Everyone,

I am going through a modal analysis in Ansys Mechanical and have started out with a problem that has a simple analytical solution (Free-Fixed Cantilever beam circular cross section). I did a modal analysis but putting applying a fine sweep mesh through the part and fixed support on the face of one side of the beam. My results are as follows Modes (256.36, 256.38, 1554.9, 1554.9, 2822.2, 4153.2, 4153.5, 4599.1, 7664.1, 7664.5) while analytical predicts Modes (257, 1606, 4502, 8831, 14596).

I am obviously encouraged by the first mode but I have two questions. Should I be expecting better accuracy one higher modes? Why some of the modes almost identical?

Thanks Guys,

I’m new to FEA and our expert just left the company.

 

[flash3780]

Did you look at the mode shapes? I'd imagine that you're calculating bending modes, while Ansys is calculating all modes (bending, stretching, twisting, etc.).

 

[vonMech]

I have looked at the mode shapes, and yes some of them are definitly stretching and twisting modes. Is there some what to supress this solutions and just aquire the bending moment solutions?

 

[flash3780]

Not that I'm aware of. They're real modes; Ansys doesn't differentiate when it calculates mode shapes.
You can calculate twisting and stretching modes by hand as well. Stretching is easiest: omega = sqrt(k/m) where k is the stiffness of the beam (k*delta/L).
Also, you'll probably get closer to the theoretical values if you loosen up your constraints where the beam is tied down. Perhaps if you constrain the beam in the axial direction at the fixity. Of course, you'll have to tie it down in the other two directions as well; you may want to split the fixed face into four quadrants and fix the horizontal split in the vertical direction and the vertical direction at the horizontal split. That will allow for Poisson expansion/contraction.

 

[flash3780]

erm... where k is the stiffness of the beam (E*delta/L)... sorry about that.

 

[vonMech]

Success! Thanks flash3780, I was able to match the analytical solution and find more information in the worksheet area. You've be a big help.

Cheers

 

[flash3780]

No problem. Happy Ansys-ing.