Compressor Discharge Pipework Natural Frequency

[briand2]

I have an L-shaped pipework arrangement (about 3 inch diameter)connected to a compressor discharge and I want to see if I can calculated its natural frequency. Details are roughly as follows (starting at the top):

Vertical pipe; copper; 20in long
Vertical flexible connector (corrugated); 20in long
Vertical pipe; copper; 20in long
Pipe elbow; 90 degrees, turning to horizontal
Horizontal pipe; copper; 20in long
Horizontal flexible connector (corrugated); 20in long
Horizontal pipe; copper; 20in long
Solid anchor, preventing movement in any direction.

The L-shaped pipework arrangement is subject to vertical and horizontal periodic forces at the top end. What I'm trying to determine is how close a / the natural frequency of the L-shaped pipework arrangement may be to the forcing frequencies (which are either 25Hz or 50Hz).

If your response is fairly general, I'm sure I can find the stiffnesses of the components and insert them to get the real answer! I'm not sure how much to allow for self-damping, though!

Thanks,

Brian

 

[briand2]

Sorry, I forgot to mention:

The horizontal forced vibration is perpindicular to the plane of the L-shaped pipework!

Brian

 

[GregLocock]

The damping won't affect the frequency to any great extent.

The first natural frequency of a cantilever is given by 1/(2*pi)*sqrt(k/m)

where k is the stiffness measured say 2/3 of the way along the cantilever, ie about 8 inches from the elbow in your case. m is the mass of the two 20" pipes and half of each of the corrugated sections, which I am assuming are the springs.



Cheers

Greg Locock