natural frequency of cylindrical shell with edges simply supported
natural frequency of cylindrical shell with edges simply supported
(OP)
how to calculate the natural frequency of cylindrical shell simply supported at edges.
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natural frequency of cylindrical shell with edges simply supported
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RE: natural frequency of cylindrical shell with edges simply supported
RE: natural frequency of cylindrical shell with edges simply supported
Steve1's formula looks pretty good to me for the fundamental natural frequency of a beam.
I have my doubts whether it can be easily applied to a shell or arch, where a uniform radial load would give pure axial stress, and no transverse deflections. (Presumably your worst mode would be with one half span deflecting downwards and the other half upwards).
If I could not find a reference text which gave me the solution, I would model unit length of shell as a simple pinned arch, and analyse the vibration modes using any of the commercial programs available to you.
If you have no access to such a program, try downloading a copy of CADRElite. That does simple vibration problems very well. (Its demo of a truss bridge vibrating was very impressive). I seem to recall that the downloadable copy will not permit you to save your model, but for a one off requirement that would not have to be too much of a problem.
Good luck.
RE: natural frequency of cylindrical shell with edges simply supported
For nonmenbers of the ASA they are $33 each or $59 for both. Well worth the money as these are the definitive references in the field.
The results for the requested case are too complex to present here since the results depend upon the actual shell geometry.
RE: natural frequency of cylindrical shell with edges simply supported
Blevins says that for a plain uniform cantilever the first mode is at 3.52/2/pi/L^2*(sqrt(E*I/m)) Hz
where m is the mass per unit length.
I must confess I have run into trouble with this formula in the past, it does not agree with another published source, but most people seem to agree with this one.
Cheers
Greg Locock
RE: natural frequency of cylindrical shell with edges simply supported