Radial / Circumferential Resonance Frequency of Cylinder 1

[vdubinsky]

I would like to know the analytical solution (formula) for the natural RADIAL / CIRCUMFERENTIAL resonance frequency of a cylinder. Please note that I am NOT talking about a longitudinal resonance that depends on the cylinder length (let’s assume that the cylinder has an infinite length).

I realize that it may be more than just one mode. I would like to know how to calculate the natural frequencies for both the primary and higher order modes as well.

I guess, it should be a function of the pipe ID and OD , as well as material’s properties (density, Young’s modulus, etc.).

Can you please provide a practical example of calculating the resonance frequency for a steel cylinder with certain material properties and dimensions (ID and OD)?

Thanks!

 

[btrueblood]

Oy. Not sure I've ever seen it. A classical solution would involve Bessel functions. Nasty little critters, those.

 

[GregLocock]

It's in Robert D Blevins Table 12-1 case 3 for thin walled tubes, radial modes only, and 12-2 case 5 for radial/axial modes.

Sorry, they are too long to type here, get it from a library



Cheers

Greg Locock

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