Eigenfrequencies of prestressed structures

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thschrader
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Eigenfrequencies of prestressed structures

Post by thschrader »

Continuing this german thread:
https://forum.freecadweb.org/viewtopic. ... 7&start=20

Here is a prestressed concrete beam, which I had to recalculate last year.
Question: does the prestressing affect the (first) eigenfrequency?
PiPlatte_Eigenfrequenz.FCStd
(49.35 KiB) Downloaded 26 times

Workflow:
open file, remesh, write the Static inp.
Edit inp, check density, add *END STEP to *STATIC calculation
add *FREQUENCY, PERTURBATION
The parameter Perturbation forces ccx to take static prestressing into account.

Result: practically no difference of eigenfrequencies for the design value of 865 kN prestressing.
You must increase prestressing to more than 2000 kN to get an effect, 3,3 to 2,6 Hz.
2000 kN is 50% of buckling load. Which is unrealistic, the beam would break.
From an intuitive point of view I would geuss that the prestressing "stiffens" the beam (which is true for
the static case), but the first eigenfrequency drops.
prestressed_beam.JPG
prestressed_beam.JPG (135.76 KiB) Viewed 981 times
input_deck.JPG
input_deck.JPG (76.36 KiB) Viewed 981 times
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NewJoker
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Re: Eigenfrequencies of prestressed structures

Post by NewJoker »

Which version of CalculiX do you use ? When I submit this in ccx 2.19 or 2.20 I get:
- with preload: 2.603266 Hz
- without preload: 3.668205 Hz

The frequencies are quite low but the effect of preload is clearly visible.

Do you have some analytical calculations for this case ?
thschrader
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Re: Eigenfrequencies of prestressed structures

Post by thschrader »

NewJoker wrote: Tue Aug 02, 2022 1:07 pm Which version of CalculiX do you use ? When I submit this in ccx 2.19 or 2.20 I get:
- with preload: 2.603266 Hz
- without preload: 3.668205 Hz
The frequencies are quite low but the effect of preload is clearly visible.
Do you have some analytical calculations for this case ?
Yes, 1. eigenfrequency without prestress/paload is 3,66. My 3,3 is a typo, sorry.
See first case in my post, same result.
spooles.JPG
spooles.JPG (10.53 KiB) Viewed 870 times
I use ccx-spooles solver. With ccx the Modal-analysis does not run. See here
https://forum.freecadweb.org/viewtopic. ... 2&p=530143

I will do an analytical calculation for the beam, but only without prestress
and for eigenmodes 1+3. Second eigenmode ist torsion...
thschrader
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Re: Eigenfrequencies of prestressed structures

Post by thschrader »

Here is the analytical calculation for the first 2 eigenmodes.
This corresponds to ccx eigenmodes 1+3. Eigenmode 2 is torsion.
No prestressing, no payload.

ccx: 3,67 Hz, 14,2 Hz
analytics: 3,72 Hz, 14,89 Hz
Matches pretty well, I think.
So far so good...
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NewJoker
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Re: Eigenfrequencies of prestressed structures

Post by NewJoker »

thschrader wrote: Tue Aug 02, 2022 4:05 pm No prestressing, no payload.
There are analytical formulas also for beams with axial load. According to "Formulas for Natural Frequency and Mode Shape" by R.D. Blevins, in this case, the first natural frequency with a compressive load of 4240 kN will be 2.6688 Hz so very close to the result from CalculiX.
Jee-Bee
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Re: Eigenfrequencies of prestressed structures

Post by Jee-Bee »

This is a realy old issue: https://forum.freecadweb.org/viewtopic.php?f=18&t=20392 (I mean that it up till now to do a Frequency analysis with forces applied)
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