Frequency analysis of pipe - comparison with hand calculations - strange results

#1

Dear Forum,

I am new to SimScale and are currently evaluating SimScale for the company I work in. I am experienced in CFD having used various codes in engineering and research for about 10 years (including OpenFOAM). I am however, a novice in FEA. Firstly, I wanted to do a simple frequency analysis of a pipe (2’’, Schedule 10S, 2000mm, titanium grade 2) and compare it with hand calculations. However, I am getting some strange results. I started by doing a mesh convergence test and got results as expected, mesh convergence was achieved with a reasonable mesh. The results for the first mode compares well with the hand calcluations, but the second mode is way off. The hand calculations yields a first mode eigenfrequency of 86.7, while the FEM-results yields a value of 85.91 (less than 1 % off). The second mode from the hand calculations is 239, and the thrid mode is 469. Results from FEA is listed below.

Eigenmode Eigenfrequency
1.0 85.91846
2.0 85.94912
3.0 233.0151
4.0 233.1042
5.0 447.498
6.0 447.6537
7.0 721.7241
8.0 721.9563
9.0 724.851

My hand calculations can off course be wrong, or my interpreteation of the results, but I find it very strange that the FEA results seems to yield results for mode 1 and 2 which are very similar. Furthermore, the same thing can be observed for mode 3 and 4, 5, and 6, and 7 and 8.

Have anyone any input to this?

Stig

#2

Hi Stig,

The results you are observing are perfectly normal. In order to interprete them, you must bear in mind that you are actually analyzing a 3D problem. When you calculate by hand the oscillation of the beam, it is supposed to occur in the plane of analysis, but remember that the pipe is actually three-dimensional, so it is not constrained to vibrate in this plane, but in any plane perpendicular to the beam axis (this will be determined by the boundary conditions). Moreover, because of the symmetry of the pipe, the oscillation modes will be the same for the two perpendicular planes of oscillation, giving the “repeated” values you see in the table. You should see this if you look at the deformation figures for each mode.

#3

Hi ggiraldo,

Thank you for your reply. That makes perfect sense.

Stig

#4

Nicely explained @ggiraldo!

@Schtig, you can also try doing the frequency analysis with a second order mesh. You can see a mesh study on frequency analysis here: Beam Natural Frequencies - Mesh Study

Doing this can also help you to get more accurate results. Although your geometrical case is quite simple but it might be possible that it leads you to the non-positive Jacobian since solver used for Frequency analysis is quite sensitive on mesh quality. Nevertheless its worth a try :wink:

I hope this helps.

Best,
Ahmed