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Quick FEA results of acoustic soundboard
http://w-ww.luthiersforum.com/forum/viewtopic.php?f=10102&t=11025		 Page 1 of 1
Author:  Parser [ Tue Feb 20, 2007 10:09 am ]
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Howdy,

As I mentioned in an earlier thread...I took a few minutes on my work PC to model up a simple braced acoustic soundboard using SolidWorks. I did a quick load/displacement analysis using Cosmos Express - a limited but useful tool. Cosmos is FEA software..this allows you to quickly & accurately run stress & strain analysis. If you have the souped up version, you can also run modal analysis in order to evaluate vibration characteristics. In my previous job, I used modal analysis in design of industrial couplings & driveshafts.

Here are the assumptions/test conditions:
*load is applied at the front of the bridge
*the sides of the soundboard are fully constrained; i.e., they are not free to move at all
*this model assumes an orthotropic material i.e. the strengths and stiffnesses are the same in all directions. This is certainly not the case with wood...but Cosmos Express is limited. With better software it is possible to take grain direction & such into account.

My main intent in doing this analysis was to see the deformed shape of the soundboard. I think that even though this is not a truly accurate model...the deformed shape makes sense and I would suspect that the mode of deformation is accurate.

The images below are some screen shots I grabbed today. The deformation shown is exaggerated thousands of times in order for those of us with normal eyes to be able to appreciate it..!





Hopefully this is accurate enough to be helpful...
Author:  Rod True [ Tue Feb 20, 2007 10:16 am ]
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Cool.....

What did you use for the force? And since these are such high exaggerations, what was the actual distortion amount, say off the plane?

I've wanted to try this same thing, but don't have the $ of course to get a good fea program. I downloaded cosmos for a demo, but they wanted to much info from me before they would even unlock the demo product.

Anyway, cool stuff, thanks
Author:  Steve Saville [ Tue Feb 20, 2007 10:45 am ]
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I saw a friend's Martin do that this summer after he left it in the trunk on a hot day.
Author:  Steve Saville [ Tue Feb 20, 2007 10:52 am ]
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How is the plate edge supported? Are all the braces similarly supported? Is it easy to move the location that the braces terminate to look at tucked vs. untucked bracing?

This is great! Do yo have vibration analysis software?
Author:  Parser [ Tue Feb 20, 2007 1:59 pm ]
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Hesh - I think the main differences between parabolic & scalloped bracing would be seen best after running a modal analysis. I would expect that one type of bracing would tune the soundboard up..and the other would tune it down.    A modal analysis of something like this will tell you the first X vibration modes in Hertz (where x is the # of modes that you'd like it to calculate). Usually there are only a few dominant vibration modes..and the higher modes are not usually significant. For example...the first mode may be at 100 Hz, 2nd at 356, 3rd at 1240, etc.. A modal analysis will also show you graphically how the part will vibrate & the max deflection.

Unfortunately, I do not have access to FEA with modal analysis at this point...


I don't think it is it all impossible to model materials like wood. You just have to take the answers with a larger grain of salt than normal since the properties vary. FEA analysis of composite materials is done the same way that you would do an analysis of a wood structure.

---

Steve, although it is not shown in the pics I posted, I told software that the edges were rigidly supported. This means that there is zero deflection all along the edge of the soundboard. The braces are rigidly attached to the soundboard; i.e., the braces flex along with the soundboard.

---

Overall, I think that tweaking the brace shapes & termination would affect the shape of the "bubble"..but probably not by a whole lot. I think the best way to really see a different shape would be to use an entirely different bracing design. I wish I had more free time to get more into this...!!
Author:  snood [ Tue Feb 20, 2007 11:25 pm ]
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Hesh.
You da man!
I am doing EXACTLY the same thing:)
We need to compare notes.
I also have access to ANSYS MultiPhysics which mean I can do a modal and or harmonic analysis of any structure.

I do FEA as my day job but in the electromagnetic domain.

My goal is to model many braces as parts in solidworks (which i also have access to) and to be able to compare bracing patterns.

The method is as follows:
Draw design in SW
Import (direct) into ANSYS
Do a harmonic analysis
Iterate and optimise!

I am not so skilled in SW and I am struglling a little to get the drawing done.

Any tips pointers or indeed drawings (to put into ANSYS) would be well appreciated.

Nice work!
Barry
Author:  snood [ Tue Feb 20, 2007 11:26 pm ]
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Oops I mean Parcer......You da man!
Soz :)
Author:  snood [ Tue Feb 20, 2007 11:37 pm ]
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Also here is one i tried earlier.
This model has been developed in SolidWorks and then analysed using ANSYS.

The diagram shows the first mode amplitude at 440Hz.

The model did not contain any auxillary items such as bridge, bridge plate or bracings.

I intend to add these in due course.

Barry.

Author:  gozierdt [ Wed Feb 21, 2007 5:00 am ]
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Very nice work, and not simple to include all the bracing.

I believe that this is the "longitudinal" (I forget the exact nomenclature) mode Ervin Somogyi talked about in his video. This mode has the top and bottom halves of the soundboard vibrating out of phase with each other around a line roughly through the waist of the box. He also mentioned a "transverse" mode where the soundboard right and left sides vibrate, and a "drumhead" (I know these aren't his names- maybe somebody has notes to put in the correct names) mode where the bottom bout moves up and down with the bridge near the center. According to Ervin, these are the three main modes affecting the sound.
Author:  Bob Garrish [ Wed Feb 21, 2007 7:02 am ]
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This is fantastic work. Although it's more or less the expected result, verification is important. Some real food for thought. Thank you for this.
Author:  Alan Carruth [ Thu Feb 22, 2007 7:43 am ]
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Good stuff.

Are the edges hinged or fixed? Real guitar tops are somewhere in between (of course).

In practice, once you get the braces on the top, the lower bout acts very much like an orthotropic membrane, I think. That's one of the things you adjust when you shave braces.

'Tapered', 'Straight', and 'Scalloped' bracings tend to have different frequency relationships between the three main top modes. The lowest, the 'main top' or 'loudspeaker' resonance, is probably the most effective one in terms of producing sound. It works with the 'main air' resonance as a 'bass reflex couple'.

The 'cross dipole' mode, where one end of the bridge goes dwn as the other goes up, is usually the next one up from the 'main top' mode in pitch. Because it is much less effective as a radiator of sound, owing to the phase cancelation of the two sides, it often acts as a 'cuttoff' for th power of the 'main top' mode. This effects the timbre in the mid-range, in particular. Scalloped bracing drops the pitch of the 'main top' relative to the 'cross dipole' owing to the looseness of the center of the top.

The 'long dipole' is the vibrating mode that looks a bit like the static displacement you've calculated. Since tops have to be stiff to resist that static displacement the frequency of the long dipole is usually fairly high; up around 350 Hz, say, close the the high E string pitch. It's hard to say whether this mode contributes directly to the sound very much, but it can be an important actor because of the way it couples with the 'A-1' air resonance. That's the mode that has the air sloshing the length of the box. Normally that doesn't put out much sound by itself either, but when the two are closely tuned to each other (as they often are) they will work together to produce a lot of output at some pitch. Often that will be around A-440, where there commonly is not another resonance to help out.

Real guitars are sometimes nowhere near as 'neat' as the above would imply. Asymmetric bracing, like the Martin style you've modeled, can yeild 'diagonal dipoles', rather than the 'long/cross' pair. In that case the A-1 coupling can also give you a 'long dipole', but not always.

I guess the point of this long post is that, while modeling the top vibrations is useful, it's even better if you can include the air as well. That's a lot of work, though.    
Author:  microsmurf [ Thu Feb 22, 2007 9:00 am ]
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thanks Alan for sharing that knowledge, and others for trying this simulation. One of these days when I have more time, I would like to do some of these work as well.


Check out this FEA done on a guitar


http://www.phys.unsw.edu.au/music/guitar/virtual.html


 
Author:  microsmurf [ Thu Feb 22, 2007 9:07 am ]
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On the above link, it is interseting to note that (0,0) mode shows the neck bending along with the body. I think we tend to think neck to be a non-acoustical member of the guitar, but it does show that it affects the vibrational pattern for sure.


I gues the stiffness of the neck would affect the tone of the guitar. I wonder if that is why A0/B0 mode matching in violin design affect the tone nicely? Alan, any thoughts?
Author:  microsmurf [ Thu Feb 22, 2007 9:15 am ]
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(Don't you just hate the Non Edit option?)


If you look at the back clamped (0,1) mode, you can see 'diagonal dipoles' which Alan mentioned. Looking at the bracing pattern, it looks very much like a Martin bracing to me.
Author:  Dale R. Kirby [ Thu Feb 22, 2007 10:36 am ]
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Looking at the free guitar 0,1 it looks like the back vibrates 180 degrees out of phase with the top.  I would think this would increase compression pumping of the air within the sound box.  What would that mean for various back woods of different mass and elasticity in relation to different top woods and/or bracing patterns?

Kirby
Author:  snood [ Thu Feb 22, 2007 10:21 pm ]
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Hi,
The static modal analysis stuff is very interesting however, I believe that the dynamic / harmonic analysis is much more usefull.
I hop eot be able to analyse the dynamic / harmonic response of braced guitar soundboards very soon
Author:  snood [ Fri Feb 23, 2007 6:07 am ]
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Extra modes on a 000 soundboard + bridge for now. Harmonic analysis to follow when I get chance :)

Mode 1


Mode2


Mode3


Mode4


Mode5
Author:  rlabbe [ Fri Feb 23, 2007 6:08 am ]
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I assume this was modelled as a flat top, not a domed top? I base this on the observation that the upper bout is sunken in. Certainly real guitars that are domed don't exhibit concavity in this section, or even flatness; they remain convex under string load.
Author:  snood [ Fri Feb 23, 2007 6:08 am ]
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Bring back the edit button!!!!
Author:  snood [ Fri Feb 23, 2007 6:10 am ]
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Mode1



Mode2


Mode3


Mode4


Mode5


Author:  Alan Carruth [ Fri Feb 23, 2007 7:00 am ]
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microsmurf asked:
"I guess the stiffness of the neck would affect the tone of the guitar. I wonder if that is why A0/B0 mode matching in violin design affect the tone nicely?"

I was unable to catch the frequency of the mode in the animation; dial-up is so much fun! Still, I have my suspicions....

The lowest resoant mode of the entire body, sometimes called the 'C-1' or 'first corpus' mode, mimics the action of a xylophone bar. As the headstock and tail block go 'up' the neck block goes 'down', with 'up' and 'down' in this case being relative to the plane of the top plate. Normally this mode is much lower in pitch than the Helmholtzian 'A-0' resonance, which is the lowest mode that can actually radiate a useful amount of sound. However, if the neck is stiff and the headstock light the C-1 mode can be as high as the A-0.

In that case, the two will couple usefully. As the head and tailblock move up, there is some pressure along the top plate, and , since the top is normally arched up a little, it 'puffs out' a bit, sucking some air in through the soundhole. In the other half of the cycle, when the headstock and tailblock move down, the air is expelled. This, of course, is what the A-0 mode is doing; pumping air through the hole, and, of course, the change in air pressure on the inside of the top also pushes the C-1 mode.

When this coupling occurs the two modes push each other apart in pitch a bit. The resulting spectrum of the guitar shows a pair of relatively low peaks in the low range (say, around G-98 on the low E string), with a dip in between, rather than a single, taller one. The area under the curve, the 'total available horsepower', so to speak, is greater than it would be for the uncoupled state, and the response is spread out over the range of a few notes, rather than being mostly on one. The low end sound is 'smoother' and 'more powerful'.

Since the neck bends a lot in this mode, the stiffness and mass of it are important. A couple of mm change in neck depth can be all it takes to lose this.

These frequencies really have to match up pretty exactly for this to work, and small changes can have noticable effects when things 'nearly' or 'barely' match. Swapping machines, and even a change in relative humidity, can move you in and out of the working range sometimes. This is probably one reason some folks get all enthused about the tonal effects of using one or another type of machine, for example. It's not the particular machine, it's the way it worked on _that_ guitar.
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