Modal Analysis of a Cantilever Beam 3

[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.

 

[sdm919]

I'm not familiar with those elements, but... Assuming the same mesh for all 3 cases, the most likely causes are transverse shear deformation and mass distribution.

Transverse shear deformation is neglected in Euler-Bernoulli beam theory which assumes plane sections remain plane AND normal to the deflected axis. Timoshenko beam theory assumes plane sections remain plane, but allows the section to rotate relative to the axis. So the Timoshenko beam should be "softer", i.e. give lower frequencies.

As for mass distribution, some elements use lumped mass, some use consistent mass, some include rotatory inertia, some don't. Without going into the details, suffice to say that there are different methods, which may over- or under-estimate the "true" solution.

No matter how refined your FEM is, it only gives answers that the underlying theory allows. Different elements are formulated using different theories, so if those differences are important in your problem, you'll get different answers. You'll have to read the user's manual.

If you use an element that's consistent with your hand calculation, then you should get good agreement, but that doesn't mean you used the right calculation or the best element for your problem.