Vibration of a column

[BespokeEngineering]

Sirs-

I am designing the controls for a robot whose main structure consists of a large, upright, aluminium, pipe of ID 0.23 m OD 0.304 m. I will be exciting teh pipe at various points and would like some assistance in calculating its natural frequency. i.e. what is the formula in terms of I, E and mass. I can find the k, but after that seem to have forgotten how to find the frequency.

Thank you.

 

[MikeyP]

It depends very much on the length of the pipe and its boundary conditions. Can you provide any more information?

If the column is shorter than about 5m then the "standard" formulae (based on Euler-Bernoulli theory) will not be accurate. The deformation of the beam will be a mixture of bending and shear motion and you will have to consider the more sophisticated Timishenko beam theory.

"Formulas for natural frequency and mode shape" by RD Blevins has expressions for a range of idealised cases.

M

--
Dr Michael F Platten

 

[GregLocock]

Guessing that the most important mode will be cantilever bending, with a tip mass, you can just work out the tip stiffness and use that in f=1/(2*pi)*sqrt(k/m)

Other frequencies may cause problems, but this will be the dominant one.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.