Hi dave,

As per your below quote in coade forum

"I think the major difference lies in the coarse versus fine mesh but not for the obvious reason. The coarse mesh leaves a greater amount of mass placed at the end points. These end points are anchored (the way I modeled them) and that eliminates that (anchored) mass from the model. Less mass leads to higher frequencies (for the same stiffness).
I think the bends, too, affect the mass distribution more so than the system stiffness."

I found that with finer mesh ( 5 element)in a cantilever beam anchored at one end,i am getting higher frequency than a course mesh(1 element only)

Can you through some light on this?

Perhaps you are taking that quote out of context here. I believe the topic of that quote is related to missing mass, not mass distribution.

I agree, CAESAR II will give a lower first mode for the coarse model. It may have less mass but the stiffness used in the coarse model is, effectively, much lower as well. You can estimate the coarse model first mode (in radians/second) by SQRT(K/M) where M=(total mass)/2 and K=3EI/L^3 with L=total length.

Thanks for your reply Dave.

1.What is the formula for estimating other modes (2nd,3rd etc) of frequency?

2. Can we apply the same formula forestimating frequency first mode for a real 2d/3d piping stress system by adding all the effective masses & dividing by stiffness?

3.Also i checked i am getting the same frequency (1st mode) for a cantilever beam anchored at one end & with/without support at other end.My thinking was that adding +y support at other end will inc the stiffness & hence frequency.what could be the reason for that?

Pls Advise.

1. For a simple cantilever, the calculated natural angular frequency of mode "n" is:
omega = [(0.597*n*pi)^2]*SQRT[EI/(m*L^4)]
2. No
3. Your cantilever is symmetric. Let's say that the pipe is running in X. You will have two identical natural frequencies each with its own mode shape - one in Y and one in Z (or two other mode shapes orthogonal to one another). If you add an end support in Y, you will change the frequency of that Y mode but the Z mode shape is unaffected and that natural frequency will remain.