## 4 DOF Model

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Trevor Gore
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### Re: 4 DOF Model

Dominic wrote:When we calculate the Di's for each increment, do we also need to do the same with the Ys...
trevtheshed wrote:I just checked my spreadsheets: I used COMPLEX to get the D's, IMSUM to evaluate the determinants, IMDIV for the y's, IMPRODUCT for the p's; and there is a value for each of these parameters for each frequency value.
trevtheshed wrote:I just checked my spreadsheets again because I couldn't recall any nested IM functions. I had a bunch of columns hidden (not noticed before, with current half speed brain!). So the determinants are a bunch of IMPRODUCTs in separate columns and then these are IMSUMed and that's how I avoided nesting things.
Basically, yes, for all of them.

Dominic
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### Re: 4 DOF Model

Cool thanks Trevor. I did read through all your posts again carefully after I had asked the question and I found those two quotes but I am not allowed to edit my own posts ...for it is written. Too many late nights playing with excel and my brain needed a break to gain some perspective. Now I can visualise what needs to be done, as long as Os' equation is correct and allows us to create a real number.
Cheers
Dom
You can bomb the world to pieces,
but you can't bomb the world to peace!

johnosb
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### Re: 4 DOF Model

That's what I did, calculate the magnitude (plot in the post above). It can't be too far wrong as it does exactly what you'd expect (well as near as I can tell). Changing the parameters changes the modes/levels, if it wasn't for the fact that the overall shape doesn't match yours on P2-37 I'd almost think that it was working!!

Os

Trevor Gore
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### Re: 4 DOF Model

Well, John, I think you're there, or very, very nearly. Well done! Sorry about that last bit. Not sure why that didn't get into the book!

Some of the residual differences may be computing "differences". For example, my computer (Toshiba Tecra running XP) gives:

αat (alpha at) = 2512.222087
αab = 2336.950779
αbt = 15972.83733

...which for a simple multiplication are some quite big differences from your numbers. (I used your values in my model, BTW, and it made very little difference, but if this sort of thing is happening on every operation, you can imagine what would result).

I tried a few quick changes, but no simple change would come up with anything that gave a closer approximation to your curve. It seems it would have to be changes across a number of areas that are required, hinting that the issue may be in the calculations/rounding etc. I guess you could have a go at doing the same and see if anything points to one of us making a coding error.

When I was putting this stuff together, one of the early things I did was to code up and replicate Christensen's Fig 3 results from his 1984 paper (full ref. in the book). I matched his curves pretty well exactly, so I felt reasonably confident that the way I approached that was OK and approached the 4-DOF model calcs the same way. Maybe that's something you could try, which might check out the computers a bit.

Anyway, a good effort, mate. I'm off to get some shut-eye.

johnosb
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### Re: 4 DOF Model

trevtheshed wrote:Well, John, I think you're there, or very, very nearly. Well done! Sorry about that last bit. Not sure why that didn't get into the book!
It was probably not required for those less mathematically challenged. I'm sure there's whole bunch of people out there that have already got it up and running without having to hassle you like us thick heads.
trevtheshed wrote: Some of the residual differences may be computing "differences". For example, my computer (Toshiba Tecra running XP) gives:

αat (alpha at) = 2512.222087
αab = 2336.950779
αbt = 15972.83733

...which for a simple multiplication are some quite big differences from your numbers. (I used your values in my model, BTW, and it made very little difference, but if this sort of thing is happening on every operation, you can imagine what would result).
Interesting...
I just hand calculated the alpha products based on your input parameters and got:

alpha at = 2515.72187
alpha ab = 2340.20639
alpha bt = 15972.8378

in the spreadsheet I calculated the area and mass values of the air plug and the value for k and had

alpha at = 2506.61132
alpha ab = 2331.73146
alpha bt = 15792.83733

by removing the calculation and changing the parameters to the values in the book I got the same as the hand calculations. If you used Excel to do the calculations then I suspect you are right and it's all to do with rounding as I know that regardless of how the cell is formatted Excel keeps the full value to n significant digits in memory and uses that value in further calculations. It probably doesn't fully explain the plot shape but it certainly wouldn't help as I am wondering about how this problem could be compounded by the IM functions given that there is probably a lot of rectangular to polar conversions and vice versa going on in the background

I've copied all the intermediate values to the front sheet of the spreadsheet and attach it to give you an idea where I'm at.
trevtheshed wrote: I tried a few quick changes, but no simple change would come up with anything that gave a closer approximation to your curve. It seems it would have to be changes across a number of areas that are required, hinting that the issue may be in the calculations/rounding etc. I guess you could have a go at doing the same and see if anything points to one of us making a coding error.
I think any coding error will be mine. I've passed my spreadsheet to Dom and asked him to go through it and see if fresh eyes can see anything. It's easy overlooking the obvious when reviewing your own work.
trevtheshed wrote: When I was putting this stuff together, one of the early things I did was to code up and replicate Christensen's Fig 3 results from his 1984 paper (full ref. in the book). I matched his curves pretty well exactly, so I felt reasonably confident that the way I approached that was OK and approached the 4-DOF model calcs the same way. Maybe that's something you could try, which might check out the computers a bit.
I'll look it up and get onto it.
trevtheshed wrote: Anyway, a good effort, mate. I'm off to get some shut-eye.
Thanks, it's a lot of fun in some sort of masochistic way. A bit of a way to go yet but very much appreciate your kind assistance.

Os.
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Trevor Gore
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### Re: 4 DOF Model

John, the D's are all a function of ω, so how are you handling that? In your last post you must have them evaluated at a particular frequency?

johnosb
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### Re: 4 DOF Model

trevtheshed wrote:John, the D's are all a function of ω, so how are you handling that? In your last post you must have them evaluated at a particular frequency?
ω (2piF) - in fact all the values on the screenshot - is the result of the 100Hz entered in the input box. The table (off screen) auto inserts all the values from 0.65Hz to 500Hz and obtains the output value for that frequency from the Db cell and plots those values. Any of the parameter values can be changed manually without effecting the plot as the plot is generated solely by the table using the rules set up by the what_if/data table function.

Trevor Gore
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### Re: 4 DOF Model

Ah, right! You did mention that. I'll drag my 100Hz numbers out as soon as I can.

Dominic
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### Re: 4 DOF Model

Hey Os, I'm about half way through recalculating everything. I've written out the equations in mathtype directly from the book then create new formulas based on those specifications for each variable then checking against your workbook. Once I have equations for one frequency I'm happy with I'll copy it across manually and see if I get different answers than what'if. Pretty much checking from first principles. No obvious mistakes yet but if there are any I'll find them. Looking for equations that might be wrong as well but nothing seem inconsistent yet.

You are right though, it is fun. And deceptively complex. Good brain gym.

Cheers
Dom
You can bomb the world to pieces,
but you can't bomb the world to peace!

Trevor Gore
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### Re: 4 DOF Model

OK, here they are:

Dt 57535.9078102831+1884.95559215388i
Ds -117827.340834859+6283.18530717959i
Db 107748.740785237+4398.22971502571i
Da 134.116591266459+8.79645943005142i
Dbar 2.31298863526292E+015-3.13890440436301E+016i

yt 8.92142530804812E-007-1.06182023060313E-004i
ys -3.60260052415647E-006+4.21352341350602E-006i
yb -2.97308070238133E-006+7.88220882586067E-006i
ya 1.20465668054809E-004+1.56376242027309E-003i

It seems to agree, reasonably, up to the real part of Dbar. I checked my coding for Dbar and it seemed OK.

johnosb
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### Re: 4 DOF Model

trevtheshed wrote:Dt 57535.9078102831+1884.95559215388i
Ds -117827.340834859+6283.18530717959i
Db 107748.740785237+4398.22971502571i
Da 134.116591266459+8.79645943005142i
Dbar 2.31298863526292E+015-3.13890440436301E+016i
Yup, problem starts as soon as I hit the IM functions. I think there must be something about the way I am using them. I took your value for Dbar and inserted it and the Y values went wacky. I'll pull up the help on IMProd, IMSub and IMSum and see what I'm doing wrong.

Thanks Trevor

johnosb
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### Re: 4 DOF Model

I went through the Dbar calcs last night and I couldn't find anything that stood out. I then calculated (at least using Excel but without the IM functions) a couple each of the products and then sum and subtract terms and got the same answers as with the IM functions so think I am using them ok. I'm down to thinking that I have a mistake in the method (or several) in there somewhere.
Tonight I will plug the calculated values for Yi back into Eq AII 2-25 through 2-28. I figure that once the solution to AII 2-25 equals AII 2-40, etc. then the maths must be correct.

Trevor Gore
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### Re: 4 DOF Model

Yes, the Dbar calc is massive. I did it with IMPRODUCT over 11 columns and then used IMSUM.

johnosb
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### Re: 4 DOF Model

trevtheshed wrote:Yes, the Dbar calc is massive. I did it with IMPRODUCT over 11 columns and then used IMSUM.
You're not wrong!

I broke it down to 21 rows and annotated it as I kept losing track. Plenty of scope for errors though. Hopefully Dom will pick up my blunder as I am going bleary eyed looking at it.
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Dbar.JPG (103.67 KiB) Viewed 39369 times

johnosb
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### Re: 4 DOF Model

johnosb wrote: Tonight I will plug the calculated values for Yi back into Eq AII 2-25 through 2-28. I figure that once the solution to AII 2-25 equals AII 2-40, etc. then the maths must be correct.
Done this and found that there are about 12 orders of magnitude difference between yt at Eq AII 2-40 and plugging in the y values into AII 2-25. No small difference, you'd reckon it would be easy to find

kiwigeo
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### Re: 4 DOF Model

Building the bldi guitar will be the easy part
Martin

johnosb
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### Re: 4 DOF Model

You're right Martin. This is all your fault from memory after I asked a simple question about a hybrid classical build for SWMBO on the woodwork forum. wasn't it you that suggested getting into the books?

Quote from the WWF:

"You're playing around with the design of the guitar. Rather than make it a stab in the dark experiment why not turn it into a more planned exercise by reading Gore and Gilet's books before you get started. Im currently doing a falcate classical build based largely on G and G's methods.

Given a choice of spending \$200 on the books or a master grade spruce top set Id go for the books any day."

See what you started, thanks for that!!

Dominic
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### Re: 4 DOF Model

Don't worry Os, I'll track down the problem. I think of it this way, once I have got equations working for all the models in the book there are none left to do and its a real buzz getting it to work.
I've finished to intonation spreadsheet and just need to load a set of strings and run it. So this model is the last cool fun bit from the book. I want to savour it.
Cheers Dom
You can bomb the world to pieces,
but you can't bomb the world to peace!

johnosb
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### Re: 4 DOF Model

Dominic wrote:Don't worry Os, I'll track down the problem.
Cheers Dom
Yeah well I think the balls in your court, I'm running out of ideas. I've even spent 2 hours working out the determinants just in case there was a misprint in there somewhere (a couple more zeros in the Dbar matrix would have been nice Trevor!!),

I think Martin's right, time to lay it aside for a bit and make some shavings. I might thin some plates tomorrow. I'll come back to it in a few days and hopefully by then you'll have solved it Dom. I got the Christensen/Vistisen paper too so might start reading that.

kiwigeo
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### Re: 4 DOF Model

johnosb wrote:You're right Martin. This is all your fault from memory after I asked a simple question about a hybrid classical build for SWMBO on the woodwork forum. wasn't it you that suggested getting into the books?

Quote from the WWF:

"You're playing around with the design of the guitar. Rather than make it a stab in the dark experiment why not turn it into a more planned exercise by reading Gore and Gilet's books before you get started. Im currently doing a falcate classical build based largely on G and G's methods.

Given a choice of spending \$200 on the books or a master grade spruce top set Id go for the books any day."

See what you started, thanks for that!!
Guilty as charged M'Lud!
Martin

Dominic
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### Re: 4 DOF Model

Well I have spent days and nights on this and it does not seem to matter which way we calculate Dbar it comes out the same and Os and I are getting the same results. I built the calculations from scratch using the equations in the book as a guide. So we have arrived at this outcome independently. But I had a dream about it last night so its time to put it away for a while.
Cheers
Dom
You can bomb the world to pieces,
but you can't bomb the world to peace!

kiwigeo
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### Re: 4 DOF Model

Anyone tried the calculations on a Mac?
Martin

charangohabsburg
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### Re: 4 DOF Model

kiwigeo wrote:Anyone tried the calculations on a Mac?
Markus

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It's only the others who suffer.

Trevor Gore
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### Re: 4 DOF Model

I checked the Dbar calc (yet again) and I have it coded exactly as per the book. So,
idunno.gif (4.39 KiB) Viewed 39294 times
I've run this stuff on three different machines, a Toshiba Satelite Pro and my current Toshiba Tecra M5 (both running XP and Office Pro 2002) and a Lenovo running Windows Vista and Office 2007. Same answers as published.

Beats me!

Dominic
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### Re: 4 DOF Model

Hi Trevor, I suspect it is something to do with the rules and how we apply them to Dbar. I am still trying different things. I've got your 100Hz numbers to work at.
Thanks for your help so far. I'll crack this eventually.
Cheers
Dom
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but you can't bomb the world to peace!

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