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Spherical shell eigenfrequency analysis with static internal pressure
Posted Apr 15, 2011, 6:28 p.m. EDT Acoustics & Vibrations, Modeling Tools & Definitions, Parameters, Variables, & Functions, Structural Mechanics Version 4.1 4 Replies
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My student and I are trying set up a model to investigate how the vibration response of a fluid-filled spherical shell changes with the static fluid pressure. We have a corresponding lab experiment with a 15 cm diameter aluminum shell filled with water that shows a 10 kHz peak shifting about 2 Hz for every 10 psi increase in water pressure.
Changing the fluid pressure inside the shell in COMSOL has no apparent effect on the eigenfrequencies. Although this is a case of prestressing the structure, the displacement is tiny compare to other models with a static load that I've read about in this forum. I'm not sure that the Buckling Analysis procedure applies here. We've been using acoustic-structure interaction in the Acoustics module, but we do not currently have the Structural Mechanics module.
In order to follow the procedure of solving for stress/strain due to the static pressure, then using that as an initial condition for the eigenfrequency analysis, is it necessary to have the Structural Mechanics module? Can this be done within the Acoustics module (or the basic COMSOL package)?
Any insight will be greatly appreciated.
Andy
Changing the fluid pressure inside the shell in COMSOL has no apparent effect on the eigenfrequencies. Although this is a case of prestressing the structure, the displacement is tiny compare to other models with a static load that I've read about in this forum. I'm not sure that the Buckling Analysis procedure applies here. We've been using acoustic-structure interaction in the Acoustics module, but we do not currently have the Structural Mechanics module.
In order to follow the procedure of solving for stress/strain due to the static pressure, then using that as an initial condition for the eigenfrequency analysis, is it necessary to have the Structural Mechanics module? Can this be done within the Acoustics module (or the basic COMSOL package)?
Any insight will be greatly appreciated.
Andy
4 Replies Last Post Apr 18, 2011, 2:58 p.m. EDT
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Posted:
1 decade ago
Hi
I would rather ask myself what is making my frquency to change ?
- Aluminium sphere expansion under the pressure, hence mass/inertia change;
- stress induced effects (but that is materials science non linearities) are they there;
- compression of the water (probably not that important at this level TBC, well perhaps important: do you not have a mach number around "pi" there ? if I remember my formulas right, for the liquid) ,
- or ...
If you apply a static pressure you will normally not see any changes for the eigenfrequency as the latter is a linear process and only elements that couple to u,v,w, lambda (or for frequency domain solvers via iomega) will have an effect.
Therefore you must either have material properties that are related to "p" and that acts on the mass or vicuosity if this enters the equations to see any changes. Note that Damping must be set up specifically
I have a model on the forum, that I'm working on, it's not yet tested out correctly, but it could be an approach, even if its rather for the opposite: canteliever in a static, large, fluid, usig the added mass from the fluid as boundary load
www.comsol.eu/community/forums/general/thread/16753/
As I do not have the accoustic module I have to live with structural ;) It would be nice to have someone reporting back here on the Forum examples of "simple" physics using COMSOL as a high end physics calculator (for some time we had some challenged coming from Alaska).
Not all problems need to fully couple fluids and structural and ... . Sometimes one physics and a few clever equations are enough, and gain a lot of time. But these need to be validated and I do not have a bunch of motivated students waiting to be feed on funny problems, unfortunately
--
Have fun COMSOLING
Ivar
I would rather ask myself what is making my frquency to change ?
- Aluminium sphere expansion under the pressure, hence mass/inertia change;
- stress induced effects (but that is materials science non linearities) are they there;
- compression of the water (probably not that important at this level TBC, well perhaps important: do you not have a mach number around "pi" there ? if I remember my formulas right, for the liquid) ,
- or ...
If you apply a static pressure you will normally not see any changes for the eigenfrequency as the latter is a linear process and only elements that couple to u,v,w, lambda (or for frequency domain solvers via iomega) will have an effect.
Therefore you must either have material properties that are related to "p" and that acts on the mass or vicuosity if this enters the equations to see any changes. Note that Damping must be set up specifically
I have a model on the forum, that I'm working on, it's not yet tested out correctly, but it could be an approach, even if its rather for the opposite: canteliever in a static, large, fluid, usig the added mass from the fluid as boundary load
www.comsol.eu/community/forums/general/thread/16753/
As I do not have the accoustic module I have to live with structural ;) It would be nice to have someone reporting back here on the Forum examples of "simple" physics using COMSOL as a high end physics calculator (for some time we had some challenged coming from Alaska).
Not all problems need to fully couple fluids and structural and ... . Sometimes one physics and a few clever equations are enough, and gain a lot of time. But these need to be validated and I do not have a bunch of motivated students waiting to be feed on funny problems, unfortunately
--
Have fun COMSOLING
Ivar
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Posted:
1 decade ago
Even if the displacements are very small as in your case, the pre-stress can in some cases significantly change the natural frequencies. In the case of a pressurized spherical shell, the change in frequency is dependent on the thickness of the shell. You should solve the static case, and follow that with an eigenfrequency analysis as you indicated. However, I believe you need the Structural Mechanics module in order to account for the effect of initial stresses on the frequencies.
Nagi Elabbasi
Veryst Engineering
Nagi Elabbasi
Veryst Engineering
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Posted:
1 decade ago
Ivar and Nagi - thank you for your helpful comments. In particular, I needed some confirmation that we couldn't do the method of using the solution with static internal pressure as the initial condition for the dynamic problem without the Structural Mechanics module.
Regarding the physics -
I was under the impression that prestressing the shell with internal pressure had some effect on the elastic modulus. Expansion of the shell and extra mass loading due to the injection of (a very small amount of) fluid would lower the frequency, not raise it. But I hadn't considered shell thinning as a possible mechansim. However, a bit of geometry and algebra convinces me that the shell thinning due to the injection of a small amount of water has a negligible effect on the resonance frequencies. At least, according to cylindrical shell theory. Also, my shell is not super thin: h/r = .04.
Does anyone have references for spherical shell theory that includes internal pressure effects?
Andy
Regarding the physics -
I was under the impression that prestressing the shell with internal pressure had some effect on the elastic modulus. Expansion of the shell and extra mass loading due to the injection of (a very small amount of) fluid would lower the frequency, not raise it. But I hadn't considered shell thinning as a possible mechansim. However, a bit of geometry and algebra convinces me that the shell thinning due to the injection of a small amount of water has a negligible effect on the resonance frequencies. At least, according to cylindrical shell theory. Also, my shell is not super thin: h/r = .04.
Does anyone have references for spherical shell theory that includes internal pressure effects?
Andy
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Posted:
1 decade ago
Hi
in the model I have started on the cantilever in a fluid, with added mass, I'm using the book of
"Vol3 Modelling of Mechanical Systems: Fluid-Structure Interaction, F. Axisa & J. Antunes, 2007, B&H-Elsevier, ISBN 978-0 750-66847-7"
I find it very good, just as the 2 other volumes, vol 4 is still missing, unfortunately
But, I have no other breating mode references, apart from a discussion a few years ago on the Forum (try a search) that made me work hard without full conclusions. I hadnt really studied such problems before, so I found it interesting to make up my mind: not finsished yet ;)
Full FSI models are in my mind often an overkill and too complex to solve quickly, a simpler (certainly less complete) approach à la "added mass" would be better. Unfortunately, I do not have the acoustic module, that could contain part of the solution all pre-cooked by COMSOL, it's certainly on my wish list, even if I'm not really active within the field of accoustics
--
Good luck
Ivar
in the model I have started on the cantilever in a fluid, with added mass, I'm using the book of
"Vol3 Modelling of Mechanical Systems: Fluid-Structure Interaction, F. Axisa & J. Antunes, 2007, B&H-Elsevier, ISBN 978-0 750-66847-7"
I find it very good, just as the 2 other volumes, vol 4 is still missing, unfortunately
But, I have no other breating mode references, apart from a discussion a few years ago on the Forum (try a search) that made me work hard without full conclusions. I hadnt really studied such problems before, so I found it interesting to make up my mind: not finsished yet ;)
Full FSI models are in my mind often an overkill and too complex to solve quickly, a simpler (certainly less complete) approach à la "added mass" would be better. Unfortunately, I do not have the acoustic module, that could contain part of the solution all pre-cooked by COMSOL, it's certainly on my wish list, even if I'm not really active within the field of accoustics
--
Good luck
Ivar