Hello,

Wondering if someone can explain a simple matter (not for me).

I have four models, (1.5" OD)

1a. Small leg vertically (Y) up (3.5") to a 3" rad. bend that turns into X and continues 15" from the bend tangent intersection point.
1b. Same as 1a but the 15" long pipe is split into 10 elements.


2a. Same as 1, but no bend, only two straight pipes forming the turn.
2b. Same as 2a but the 15" long pipe is split into 10 elements.

The results from a simple modal analysis are as follows:
(Only first mode frequency reported)

Model 1a/845 Hz
Model 1b/970 Hz

Model 2a/1310 Hz
Model 2b/1290 Hz

My questions:

a. Why are there opposing trends between the two types of models (one type has a bend and the other only pipes), i.e., the first frequency increases (845 to 970 Hz) when there is a bend, but decreases (1310 to 1290 Hz) when there is no bend?

b. Also, why is the starting frequency so much different between models 1a and 2a?

c. Specifically, how does the modal analysis treat a bend vs. a pipe in this example?

Btw, lumped mass or consistent mass models did not change the trend.

My client claims that NASTRAN does differently. I do not have the numbers yet from it.

Thank you very much for your input.

At more nodes in a strait lenght ==> more accurate and higher the calculated first frequency.
A bend have not the same stiffness as 2 strait element.
2 strait elements istead of a bend element will be stiffer and higher frequency.

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.

Thank you for your responses.

I was hoping to learn how the bend mass (or flex factor) is distributed so I can explain why the different behavior shows only for the first mode (in a bend model), and not for the other modes nor a pipe only model?

Why does the first frequency alone increase (845 to 970Hz.) with a finer mesh (with MORE mass participation), when the commonly observed (and explained) fact is that the frequencies decrease with a finer mesh (incl the first one) because of more mass participation?

Thanks again.

A simple example :
A beam on side full restraint.
D = 88,9 mm
t = 6,0 mm
E-Modul 210 000 N/mm2
rho 7,85 kg/dm3
L 2000 mm

At Euler Beam Theorie
first eigenvalue:

f = 0,56 * (1/L*L) * sqrt (E*I/rho*A)
Theoretical f = 21,28 Hz

Now calculat the first eigenvalues with Caesars eigensolver
with 1,2,4,8 Elements.
You can see the Tendenz.
This show : More elements higher first eigenvalue and approach to theoretical f = 21,28 Hz.
So much the better your mass discretation ==> exacter the frequency by the solver.