Modal analysis of a simple cantilever beam

[cspkumar]

Hi,
I ran a modal analysis of a hollow rectangular section cantilever beam with beam4, beam8 and beam188 elements. Beam4 and Beam44 produced the same frequencies for bending modes and match closely to hand calculations. But results with Beam188 differ by ~30%. Can anyone explain the reason for this behavior?

Thank You.

 

[Stringmaker]

The difference you're seeing is due to the theory which goes into the element formulation. Older beam elements such as BEAM4 and BEAM8 are based on Euler-Bernoulli beam theory. Newer beam elements, such as BEAM188 are based on Timoschenko (shear-deformable) theory. Do a little searching on the web or through an old text book if you'd like to know what those theories are based on exactly. For most applications BEAM188's are probably a better choice...but that's just my opinion.

Good luck,
-Brian

 

[cspkumar]

I knew about the theories behind the beam elements. I thought shear deformation does not play any role in modal analysis. But the results contradict this. Why?

Thanks.

 

[meshparts]

Hi cspkumar,

are you shure, teh real constants of the beam8 and beam44 are correct?

Regards,
Alex

 

[cspkumar]

The moment of inertia's are exactly the same for Beam4, Beam44 and Beam188 elements. Also, modeled with shell elements and the frequencies are different. If E, I and m are the same then, frequencies should be the same I thought, correct?

Thanks.

 

[pja]

What your length to thickness ratio? If it is larger than say 10 then shear deformation isn't the reason for the difference...even though shear deformation is taken into account in modal analysis. It's a linear effect. Anyway are you sure your results are mesh converged? I didn't check but I think that beam188's use lower order polynomials in bending than beam4's so they may converge slower.

 

[cspkumar]

The slenderness ratio is well above the minimum. Increasing the mesh density did not change the frequencies in beam188 elements.