natural freq. for beam with non-uniform cross-section

[jbw9]

Hi,

I would like to model a cantilever beam in a program like MathCAD that I can modify quickly. It seems silly using FEA (Nastran) to model this type of system just to get the first few modes and mode shapes.

I have been able to do this for a simple uniform beam using the flexural matrix and mass matrix, obtaining the eigenvalues and eigenvectors. However, I am having a hard time figuring out the best way to tackle the non-uniform cantilever beam. The example I am working is a section of pipe, coupling, another section of pipe (diff. schedule), and a large mass at the free end. I need to model the details b/c the solution needs to be very accurate. PLEASE HELP!! Thanks in advance.

I have attached a schematic.

 

[FeX32]

Why is it silly to use FEA for such a problem?
In theory, a distributed parameter model would be the most accurate. Unless you are familiar with solving coupled PDE's then FEA is the easiest.
Although, if it were me, the first thing I would start with is lumping the pipe sections and then solve the lumped parameter system.
From here you can get a "feel".
Then move on to the PDE modeling.


Fe

 

[FeX32]

also, depending on how that coupling is "stationed" and made of it potentially could male your results "way off" perse is not modeled.


Fe

 

[electricpete]

If you were programming from the ground up, it is numerically simpler to solve the problem by Holzer's method, or Mykelstahd/Prohl transfer matrix method. I have programmed the latter in excel myself.

But if you already have an FEA program...

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[GregLocock]

Agree, I'd use FEA to check my handcalc. Or vice versa.

Anyway, Rayleigh Ritz is another good approach for this sort of problem, it depends on whether you'd rather use iteration (Holzer) or differentiation(R-R).

Holzer is probably better suited to mathcad





Cheers

Greg Locock

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