Dynamic FEA of a brass sheet buckling

[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 occurring 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 realize 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

 

[ZapperZ]

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

Zz.

 

[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!

 

[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 a lot 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 that's 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 a lot greater than it is at the other areas where you may not feel as much force. good luck

 

[FredGarvin]

When you say:

My goal is to describe what is occurring within the material that causes this sound.

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.

 

[ping166]

Hi Guys...Thanks for the feedback!
(Sorry for the double posting i couldn't find a way to delete the previous msg --- I am 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 that's being pitch bended. I think this is caused by the constantly changing stress across the sheet as it deforms(Hence the dynamic FEA). Weather this is something that needs to be looked at from the molecular level I am 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 I am talking about I am concentraing not on the oscillating sound that Rolf creates more what is occurring 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 occurring 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

 

[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.

 

[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.

 

[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 I am actually trying to explain.
http://www.skynet.ie/~one6six/FIles/Short.wav

Thanks again>

 

[FredGarvin]

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

 

[ping166]

Yep that sounds about right :tongue:

 

[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.

 

[ping166]

... 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 ...

..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?

 

[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 )

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 .

 

[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

 

[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.

 

[ping166]

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

 

[ping166]

Does this make sence...using eigenvalues in conjunction with the helmholtz equation 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?

 

[PerennialII]

Does this make sence...using eigenvalues in conjunction with the helmholtz equation 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?

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.

 

[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

 

[PerennialII]

Not a problem ... thanks to your highly interesting problem I'm considering doing an acoustic analysis of my living room :tongue2: . Yeah, think with Pro you can get lots done, good luck & have fun !

 

[ping166]

I back with another question...
I have been working with Pro/M for the last few weeks now and I am making good progress (FEA is far more approchable with good software ). Heres my question bearing in mind the problem I am trying to solve should i be doing modal analysis or buckling analysis?
As i discussed earlier the inital "Impulse response" came from the buckling of the material so i imagine that i should be looking at the buckling modes.
The freq's and shapes of the modes are very different between the two analysis. So which one is more appropriate?

Any suggestions?

Also has anyone used Pro/Mechanica to couple the structural and acoustic wave eq's? I have been looking through the online help files but i can't see anything that can show how to approch this...

Thanks

Ping166

 

[Antiphon]

Much of the whomp sound effect will be the result of the motion of the
plate causing a doppler shift. The FEA will not reproduce this unless you
have a solver for sound emitted from moving objects.

 

[ping166]

Does the Doppler effect really have a large effect on the sound? There is such a small movement I would have thought the doppler effect would have been negligible.I am more concerned with how the natural modes change during the course of a bending. My audio effect will be based on modal synthisis so I am hoping to get this down first. A doppler effect could be built into the program relitively easily. Thanks for the suggestion it could be important.

 

[Antiphon]

I was imagining a plate being struck and/or bent rapidly. If the plate is not moving
much then this will not be a big effect.

 

[PerennialII]

Great to hear you're making progress!

I back with another question...
I have been working with Pro/M for the last few weeks now and I am making good progress (FEA is far more approchable with good software ). Heres my question bearing in mind the problem I am trying to solve should i be doing modal analysis or buckling analysis?
As i discussed earlier the inital "Impulse response" came from the buckling of the material so i imagine that i should be looking at the buckling modes.
The freq's and shapes of the modes are very different between the two analysis. So which one is more appropriate?

If your acoustic problem is 'fed' by the buckling problem I'd then go with it, i.e. if the sound results from buckling then buckling it is ... unless you're interested about the vibration response of the buckled component ...

Also has anyone used Pro/Mechanica to couple the structural and acoustic wave eq's? I have been looking through the online help files but i can't see anything that can show how to approch this...

Haven't done that using Pro/Mechanica package so can't really help there, can however always do it by representing the solution of the mech PDE as a boundary
condition to the wave PDE.

I was imagining a plate being struck and/or bent rapidly. If the plate is not moving
much then this will not be a big effect.

Would think that the source velocity is small enough compared to wave velocity to let the Doppler untreated, especially if focusing on first mode(s). Of course depending on how & how complex the utilized coupling is can be included as well.

 

[ping166]

Natural frequencies change under load. Is is possible using software (FEMLAB or Pro/M) to model this change as a load is applied? I ask this because i can only perform modal analysis on "free" models that are unloaded.

 

[PerennialII]

If you're doing a direct modal analysis probably not, however doing a sequential analysis where you get the results along with deformed geometry to your modal model is possible for example in Femlab. Possible in one way or the other in most software, if you could define a sequential coupling analysis or an analysis with an initial state for the modal analysis the effects would be incorporated. Of course if you've a specific loading state which you want to study a transient finite deformation dynamic or a finite deformation analysis (for buckling) will get you the correct response. I'd suggest you take a look at what sort of loads etc. for example Pro/M supports in modal analysis, what sort of results it can read in as an initial state (if it reads all the results from a previous analysis in a coupling mode ... that would be best) and whether there is a sequential (or unidirectional) coupling option you could use for this purpose. Kind of adding a third stage of coupling to your analysis.

 

[ping166]

Quick question... does anyone know a formula for the elastic porential energy of a plate under axial compression?

Thanks