# Dynamic FEA of a brass sheet buckling

1. Jun 28, 2005

### ping166

Hi all,

I am a student of Music technology and for a project that I am working on I need to do an unusual FEA. I want to create a simulated model of the sound phenomenon that occurs when a sheet of material is deformed. As part of this I am required to a dynamic finite element analysis for the deformation of three types of material: a Brass, a plastic and some kind of wood. I would like have a dynamic model that could show the change in the distribution of stress across the metal as it deforms. I imagine that this should not be a very difficult thing to analyze for an experienced engineer as it is simply consists of an elliptical sheet of material that is deforming.

Please have a look at the picture to see what the system involves.

http://www.skynet.ie/~one6six/FIles/DSCN0126.jpg

It simply consists of a sheet of brass with an elliptical shape (Major axis Roughly 1 meter and Minor 60cm) that is hung from a Microphone stand via an elastic band. When you swivel the stands handle the sheet looses its rigidity and deforms under its own weight. (…and makes an interesting sound that I am trying to simulate). The sheet of metal can be substituted with a sheet of flexible wood or plastic. My goal is to describe what is occuring within the material that causes this sound. Hope fully if i can do this i will be able to write a VST audio effect to mimic the process.
My background is in computer science so I am having difficulty with the FEA side of things so I’m hoping someone out there can offer some helpful suggestions. I realise this is probably trivial and not very relivent to most of you engineers but i could really do with some help/sugestions here.Has anyone done an analysis on a simular system like this before? Can anyone out there suggest a good software package (preferably shareware) that I should use (Ansys/Lisa)?

Thanks for any help or suggestions you can provide,

Ping166

Last edited by a moderator: Apr 21, 2017
2. Jun 28, 2005

### ZapperZ

Staff Emeritus
Please do NOT do multiple posting of the identical thing. This violates PF rules. The other thread is deleted.

Zz.

3. Jun 28, 2005

### brewnog

I'm a musician and an engineer, and I'm having a bit of trouble trying to visualise what's going on.

Can you please explain more about how the sound is made? By how much is the sheet deforming? How thick is the sheet? How does it actually deform? I'm picturing a kind of Rolf Harris wobble-board, am I on the right lines?

And does this deformation cause the sound itself, or are you looking at how different loading conditions imposed on the sheet affect the sound, say, when it's struck (something akin to the difference between a crash and a ride cymbal, for instance)? I think it's the former, though.

I've not done all that much FEA so others will probably be more helpful, but I just wanted clarification on what's actually going on. I would suggest that ANSYS might be the way forward, but only because it's all I've ever used and has quite a nice interface.

Finally, may I ask how you're going to leap from a stress analysis to synthesising a sound? I'm not challenging you here, I'm just quite interested in what you're doing!

4. Jun 28, 2005

### abercrombiems02

This is actually a very complicated problem, what you are really trying to figure out are what the modes of vibration are. Essentially your best bet would be to get a motor with a controller that causes forced vibrations. When you reach a certain frequency you'll notice it gets very noisy, this is one of the structures resonant frequencies. At this point the thing should be vibrating up and down or left and right only. In the higher modes of vibration (there are more than 1) the structure will vibrate about multiple axes. The actual strain displacement field is not something you want to calculate, I suggest you get a stroboscope and with that you should be able to view displacement field and sketch it. I haven't done alot of work with any ellipses, only wings. Basically if an aircraft's wing is designed poorly, it will reach a flutter speed that causes resonance in the wings and can cause them to tear off. I know it sounds expensive and time consuming to purchase this equipment but thats the way we do it in the lab. We did model it using some FEM software but that too is not cheap and requires quite a bit of know how as to how to format all the numbers, materials, and dimensions correctly. If you want a cheap stroboscope just hold a metal screw driver over the surface, when u feel a harder hit you know the magnitude of the dispalcement field at that point is alot greater than it is at the other areas where you may not feel as much force. good luck

5. Jun 29, 2005

### FredGarvin

When you say:
I am assuming that you are talking about the vibration of the membrane, not something on the molecular level or the like.

Is there a particular interest in the elliptical shape? Like Abercrombie mentioned, you're looking at the modal responses of the plate after, what I am assuming, is an impulse, i.e. hit with a hammer or mallet. The various mode shapes of simple shapes like a circle should be pretty well documented. I have a musical engineering book that goes into drum head vibrations, which would be very similar to what you are doing except for the constrained boundary conditions. I would suggest that do some research into modal analysis and look specifically for round plates. You may get lucky enough to find something relevant. In the mean time, let me see if I can work in some time on a friend's workstation here to see if I can get a simple analysis. I can't gaurantee it, he's pretty busy.

6. Jun 29, 2005

### ping166

Hi Guys.....Thanks for the feedback!
(Sorry for the double posting i couldnt find a way to delete the previous msg --- im a newbe :uhh: )

This is indeed a complex problem I have been looking at it for a while and have heard many varying attempts to explain it. The one i was concentrating on was simular to your idea Fred. When the sheet is unloaded and standing upright (as it is in the photo) it is rigid. When you move the top of it it looses its rigdity and starts to collapse. This movement from ridigity to instability causes a responce that is simular to an impact impulse response(Though no actual external force is applied). Basicly, i look it as a 'Flexible Cymbal'. As the sheet deforms it gives what sounds like a cymbol thats being pitch bended. I think this is caused by the constantly changing stress accross the sheet as it deforms(Hence the dynamic FEA). Weather this is something that needs to be looked at from the molecular level im not sure. Could this sound have to do with the redistribution of mass as it under goes stress?It produces a strange sound and it occurs when you bend any sheet of flexable material....im sure you have heard it a million times before just never though it was worth investigating further!!
(I can post an audio file if anyone wants to hear it)

BREWNOG - If any of you have heard of Rolf Harris you know exactly what im talking about I am concentraing not on the oscillating sound that Rolf creates more what is occuring during one single deformation.

ABERCROMBIE - Thanks for the suggestion there is an aeronautical department here in my university and i will try to see if they can help me with the equiptment needed to find the modes of vibration. Is there any way to work theses out theoreticly?

FREDGARVIN - If you could help me get started on this FEA i would be very grateful.

Some background information: as I said before i am studying music technology and as part of my course I was asked to create an experimental musical instrument. Now i know this hardly looks like a Stradivarius violin but goal was to create an interesting sound and explain the physics of how it generates its sound. I have been trying to come up with a valid explination since. As part of a project that i am working on i hope to write a plug in audio effect (VST) that would be based on what is occuring in the system. The idea is to map the charracteristics of the sheet (type of material, size of sheet, shape of sheet ect) to the sound produced so that i could have presets for the plugin effect. The end restult will not be a synthisizer but an audio effect that will "warp" sound occording to what is happening in the system. I hope to controll the effect using an external MIDI controller (basicly a pitch bend wheel on a keyboard).

There is no real reason for the ellipitcal shape other than the fack that i looks good. Originally i thought that an ellipse would deform in a more uniform manner around its central axis and that this would some how make it easier to analise ....but this was just wishful thinking :tongue2:

Keet the suggestions comming.....

Thanks again

ping166

Last edited: Jun 29, 2005
7. Jun 29, 2005

### brewnog

Ok, so we've got a kind of "woomp" sound then?!

I just typed out a couple of paragraphs on why I thought FEA would be much less fruitful than analysing a recording of the sound it produces, but I've changed my mind. My advice is to pester Fred a bit more.

8. Jun 29, 2005

### abercrombiems02

I believe there is a way to find the frequencies for the first few modes, but I do not know how to do that. All I really know that it depends on the geometry of the specimen and the bulk modulous of its material. The bulk modulous is what determines the speed of sound in a given medium.

9. Jun 30, 2005

### ping166

Ok suppose i do find the first few modal frequencies..... as the the sheet deforms are these frequencies slightly increasing because of the change on stress across the sheet? This would be fairly consistant with a 'Flexible Cymbal' type of idea.....

Here is a short audio clip of the sound produced...admitedly its nothing amazing but it should give an idea of what im actually trying to explain.
http://www.skynet.ie/~one6six/FIles/Short.wav

Thanks again>

Last edited by a moderator: Apr 21, 2017
10. Jun 30, 2005

### FredGarvin

Like bending an old saw blade...Now I get it!

11. Jun 30, 2005

### ping166

Yep that sounds about right :tongue:

12. Jun 30, 2005

### PerennialII

... you could also approach it as an acoustic model, in a general case coupling the structural and acoustic PDEs (one direction more like it) in a FEA .... but the vibration analysis is probably the place to go / start.

13. Jun 30, 2005

### ping166

..This sounds interesting. The differential eq's could be used directly when writting the audio effect simulation. Would this be a difficult thing to implement? Do you have any information or refferances that could help me achieve this?

14. Jun 30, 2005

### PerennialII

.... at least many commercial software contain acoustic features (the mechanical vibration side being pretty much a given), I'd bet you can find freeware as well although in this respect I've only used commercial codes (I've done this type of analyses with Femlab, which is a multiphysics code where the coupling is easy to do). (e.g. IFER can be a good starting point http://www.engr.usask.ca/~macphed/finite/fe_resources/node12.html [Broken] )

With respect to the acoustic side of things the wave equation for acoustic waves, a Helmholz equation, can be given for example as

$$\nabla\cdot(-\frac{1}{\rho_{0}}\nabla p+q)-\frac{p\omega^{2}}{\rho_{0}c^{2}}=0$$

(symbols left to right : fluid density, pressure, dipole source, angular freq, speed of sound)

can be used to exhite the waves using the mechanical vibration analysis results as boundary conditions of the acoustic problem (like an acceleration BC).

I'd say if you're going to do an implementation from '0' for a general case I'd first do the mechanical vibration aspect and then go with this if want to go all the way, however utilizing at least pieces of existing sources may be a good idea in order to avoid the workload diverging, can happen quite easily with these things. As always, a question of how much effort you want to spend on it .

Last edited by a moderator: May 2, 2017
15. Jul 1, 2005

### ping166

My inexperiance with FEM is starting to make me feel bad :uhh:

Ill ask my leacturer if he can source some software for me....

Thanks again

16. Jul 1, 2005

### PerennialII

.... no worries, if you've access to, say, any of the 'big ones' of FEA the vibration analysis can be done with relative ease, and if you decide to go with the wave stuff a nearly similar thing. Typically you can use many software as black-boxes quite successfully (word of caution naturally always in order here) without knowing all theoretical & numerical aspects of the problem, basics will often suffice.

17. Jul 4, 2005

### ping166

Score... Ive found a lab with Pro/Engineer wildfire hopefully this should do the trick

18. Jul 11, 2005

### ping166

Does this make sence...using eigenvalues in conjunction with the helmholtz equasion to model the sound. It was suggested by an engineer friend but he was a little sketchy on the details.

Any ideas on how this might be achieved?

19. Jul 12, 2005

### PerennialII

I think it does ... the eigenvalues can be used to identify the boundary conditions for the acoustic analysis, and the eigenvalues are affected by the parameters/modifications you do in the structural analysis, so that sounds reasonable. So you'd determine the eigenvalues (focusing on lowest (deformation) mode is likely the way to go and will suffice in your analysis) and state that pressure waves are exhited in the acoustic problem via an acceleration boundary condition, i.e. a condition on
$$\frac{\partial p}{\partial n}$$

... got to look at the specific format, likely it's something like

$$\frac{\partial p}{\partial n}= \rho \omega^{2}u exp(i\phi),$$

but anyways, the frequency and the deformation mode will be present in dictating the bc. It's probably the most straightforward way of solving the whole thing.

20. Jul 13, 2005

### ping166

Excellant ...thanks Perennial.
Im starting to see the light at the end of the tunnel...I now have some sort of a basis with which to work from. I have been using Pro/Machinica for the last week and its pretty intuitive and impressive...and the animations are very usefull.
Ive a lot of work ahead but your input has been invaluable.

Wish me luck,

Ping166