Finding the natural frequency of a beam by modeling as a transverse beam.

[shreddinglicks]

I'm trying to find the natural frequency of this pipe. Assume the bends are perfect 90 degrees.



I can follow the textbook approach. Breaking the beam into 3 segments and applying continuity but I then have a 6x6 matrix to obtain eigen values from.

Is there a simpler way that can be done by hand?

 

[khansaheb]

I'm trying to find the natural frequency of this pipe. Assume the bends are perfect 90 degrees.

View attachment 39124

I can follow the textbook approach. Breaking the beam into 3 segments and applying continuity but I then have a 6x6 matrix to obtain eigen values from.

Is there a simpler way that can be done by hand?

Not that I can think of....

 

[shreddinglicks]

Not that I can think of....

Bummer, I was hoping there was something similar to the superposition used in heat or Laplace equations.