4 DOF Model

[Steve]

Thanks for keeping this going everyone, and sorry for not getting back. I took a holiday! Then there's all the other sh!t I've been having to deal with recently (nothing serious, just takes time). Anyway, there's about two days effort to go through all my workings again to check everything term by term. It's that mental fortitude thing... I'll get to it eventually...
Please keep posting.
BTW, has anyone tried yet to fit their version of the model to a guitar frequency response curve?

I've gotten too busy myself. In connection with your question, I'm wondering what parameter the main air peak is most sensitive to and whether that is possibly one of the more poorly constrained parameters. The "corrected" model still fits your plot pretty well except for the amplitude of the main air peak.

Direct answer to your question is no, not here. I don't have data that good for any of my builds so far, or any of them still sitting around to thump on.

Not here either. At the pace that I move, it feels like I won't get an opportunity to implement the model for years. Hopefully we've reached a consensus by then . Maybe you should have included a CD of the models in the sleeve with the plans . It wouldn't be nearly as much fun, but would give some consistency.
Steve

[Tom West]

Just read this..................!!! Looks like all the engineer types are having fun.!!! Think I'll stick to building guitars. Enjoy yourselves guys.
Tom

[jellicorse]

Hi all,

Just joined this forum (even if it is based on the other side of the planet), although I have been lurking here for some time.

I bought "The books" a while back and have spent the past year or so getting to grips with maths in the hope of understanding the Design Book. When I first opened that book a couple of years ago, the mathematical sections were well beyond me (I didn't even know what a differential equation was); now I can follow these things fairly well, at least so far!

Anyway, I am currently hovering around the section on the 4 DOF model and have been trying to put this together in excel. I started by following the example of early posts on this thread; only later did I realise that people have run into trouble - seemingly with the D bar determinant.... (If only I had read ahead...)

Has anyone found a way to make Excel "work" with this? I'm using the 2008 version and have tried two things: evaluating the determinant of D bar (Equ AII 2-39) step by step in Excel (and it took up A LOT of spreadsheet space to do) and also evaluating it as per Eq AII 2-44...


These are the values for Dbar I get at 100Hz (or 99.83Hz):


Evaluating the determinant step-by-step:

18269899872423500-14606803730232800i

Evaluating determinant as per Eq AII 2-44:

710297770691152-31293174150588100i


(I've also copied the working into Openoffice Calc, just to see, and the results come out the same).

There's a big difference there, and neither are close to the correct value. I've spent the best part of the day going through and checking the calculations so I don't think there are mistakes in the calculation.

It's beyond me how this can come out correctly on one person's system, but not on another's... I think I've read on here that Trevor used Excel 2003. Pretty sure my dad's got that on his computer, so next time I visit I'll have to have a go on his machine: perhaps it's just a question of the version of Excel.

If anyone has worked their way around this, or has any advice I'd be very grateful indeed!

[jellicorse]

Actually, scrub those last values (I'd changed the parameters slightly). Using the parameters from the book (p. 2-37) I get:


Dbar at 99.8Hz:

Step-by-step evaluation:

17109250024919600-14664066332842700i


Evaluation as per Eq AII 2-44:

2921776425179630-31456091755907500i

[Trevor Gore]

Well, it only took me two and a half years to get around to fixing this up! Amazing how some things are just so easy to put off...

Anyway, Jim found this problem:

Merry Christmas to all from the U.S. East Coast. I have been trying to program up the various tools in the book in matlab (I know nothing about excel), and I had been stuck trying to reproduce Figure 2.4-4 with my code. I was getting very strange behavior at 100 Hz and below. I have rederived the solution starting exactly from AII 2-1 through 2-4 as given, and I have a sign difference in one term compared to the result AII 2-43. I get

+ K_t K_b alpha_ab

Steve found this problem:

My solutions for AII 2-40 & 2-41 were the same as documented in the book, but I'm getting a different answer for AII 2-42 - for the final term on the top line, I'm getting Ds.alphaab^2, rather than Ds.alphaab.alphaat. Given my skill level in the area of matrices I'm happy to be corrected. For what it's worth, I changed my calcs for yb to see if it made a difference, but alas the numbers are similar enough that the output graphs looked exactly the same, so right or wrong, it's not going to make a difference.
Steve

..to which there was a simple answer:

Ah-ha, you found another typo in AII 2-37. That lower left element in the 4 by 4 should always be alpha_at except in y_t, where that is the column that is replaced. With a proper alpha_at in AII 2-37, AII 2-42 is correct.

The answer to Jim's first concern was as he suggested, a typo in Eqn. AII 2-43; the leading negative in the numerator should be a positive. So, if everything is coded up correctly you should get exactly what Jim posted:


...and if you keep the incorrect negative in Eqn. AII 2-43 you get this:


On page AII-9, Eqn. AII 2-37 should lead with y(sub b) and Equ. AII 2-38 should lead with y(sub a), but I don't think that was confusing anyone and thanks to whoever pointed that typo out.

So with those fixes done, you should be well set for "calibrating" your 4-DOF models to your chosen tap response.

Thanks for all the help everyone!

[Jim Kirby]

I know the feeling Trevor - someone asked me a question on what I remember was something like a truncation of this model back to 2 dof and I said I'd check it out - last March I think it was ... I've been making him wait almost as long as my most recent guitar customer

[GregHolmberg]

I know this thread is really old, but I just want to give a big "thanks" to Jim Kirby and everyone else who worked on this. And if course Trevor Gore for writing the book in the first place!

I installed the free open-source software GNU Octave (version 6.2.0 for Linux), copied the script Jim posted here, and it just worked! Plugging in the parameters from the book page 2-37, I got a graph nearly identical to the one in the book (some very slight differences, probably precision differences with the Excel spreadsheet software).

The script is surprisingly short for such complicated formulas. I hadn't realized until I looked at the Octave Workspace pane that these formulas involve multiple 1x5000 vectors (of double) and multiple 1x5000 vectors of complex doubles. Matlab and Octave are amazing. I can't imagine doing this in a spreadsheet!

This will allow me to play with different body dimensions and sound-hole sizes to target certain coupled frequencies (air, top, and back) with reasonable confidence that when I build it, it will at least be in the ball-park of those frequencies. And then I can adjust a little in the finished guitar. In addition, the script can print out the uncoupled top and back frequencies so I can target those in the separate components before I assemble the body. Fantastic!

Thanks again to everyone here! This script should be easier to find, it's so useful.


Greg

[GregHolmberg]

In section 2.4, the book references two papers by Ove Christensen. I managed to find these on the internet, in case anyone wants to read them.

Simple model for low-frequency guitar function, 1980.
Found here: https://www.iuliusguitars.com/portfolio ... -research/

An oscillator model for analysis of guitar sound pressure response, 1984.
Found here: https://www.speech.kth.se/music/smac83/ ... olume2.pdf
Since this is 345 pages, I cut out just the 16 pages of the paper.

Both PDF's are attached.

Greg

[GregHolmberg]

Can Google Sheets implement the 4DOF model? Yes, it can. It works pretty well, too. The graph appears to exactly match the output from Jim's Octave script (graph I posted earlier in this thread), and is pretty close to the book, Fig. 2.4-4. The differences appear to be in the dB values, but the frequencies of the peaks look the same to me.

4DOF spreadsheet

Anyone can view it, and see the formulas. Anyone can File->Make a copy and change their copy.

I haven't found a way to identify the db peaks though, so you have to do that manually.

I think this was the hardest spreadsheet for this book. Took me a couple of days. Although, the intonation one was no walk in the park!

I hope this helps someone.

Greg

[GregHolmberg]

Google Sheets is a bit slow on the 4DOF model (it's plenty fast for everything else). In the spreadsheet linked above, I only calculated every 1 Hz, 60 to 500, so 440 rows. This takes 9 seconds to recalc, so about 50 rows/sec, if for example, you change Kt.

In a copy of this sheet I tried every 0.1 Hz, 60 to 410, so 3494 rows, and this took 61 seconds, so about 60 rows/sec.

That's a pretty long time to wait. I want to play with the size of the box, the soundhole size, the stiffness of the top and back, and the mass of the sides, and get an instant redrawing of the graph.

So from Google Sheets I downloaded an OpenDocument (.ods) file, and opened it using LibreOffice Calc. It worked in LibreCalc no problem. Calc took just 6 seconds to recalc, so about 10X faster than Google Sheets.

I like Google Sheets a lot (very easy to use), but going forward I will be using LibreOffice Calc. It's free, it's fast, and it's got a lot of features. I especially need the solver it includes, which can solve over multiple inputs, which is necessary for the saddle/nut compensation spreadsheet.

It's shame, because Google Sheets is so easy to share--nothing to download, just view it in a web browser. I'll have to find a way to make the LibreOffice .ods files available for download.

Greg