Frequency vs. Deflection for Measuring Flexural Modulus

[NRMiller1958]

I’ve been testing all my top and bracewood to find the best combination of stiffness and density, optimize plate thickness, etc. I started using the frequency-based method from the Gore books, but since I was also testing deflection, I decided to compare the flexural modulus using that method (also with the formula from the Gore books) on the same top plates and bracewood.

Unfortunately, I’m having trouble getting a satisfactory correlation between the two methods. Here’s a plot comparing the longitudinal stiffness calculations using the 2 methods on 8 sonically tested tops from PRT. Since they don’t agree very well, I’m left with the dilemma of deciding which calculation to use to determine top thickness.

Top stiffness.jpg (42.15 KiB) Viewed 2867 times

Am I overlooking something? Has anyone else done a similar comparison with better results?

Neil

[GregHolmberg]

I've never done it myself, but here's a few threads on using deflection:

Plate target thickness of non rectangular plates using deflection testing

Re: Top thicknesses

I think the results from deflection testing will depend a lot on how flat the board is. It might make sense to measure both sides and average? Or pre-load it? Not sure.

Also, the supports must be within the rectangular portion of the board.

Greg

[kiwigeo]

Without looking into it in detail I'd hazard a guess that with the flexure test the testing procedure itself introduces some variability in results....more so than for frequency tap tests.

But we shall await the sagely wisdom of Colonel Gore

[Jim watts]

Not Trevor, he'll have a better answer for sure.
I used to statically test my tops/braces before Trevor's book came out. So its been quite a while since I've done it, but I do recall comparing the test to one another when I built my spreadsheet. As I recall the dynamic test (Ala Gore) came out slightly higher than the static test which was expected as dynamic test typically give a higher modulus value. But, the test were consistent and not radically different, so I was happy. I've continued with the dynamic testing as it's faster and his books are set up for it.
Also, you can definitely preload the top lightly which helps and don't go crazy on the amount of weight used to deflect the top.

[Trevor Gore]

It is possible to get comparative results, but you have to be very careful about how you do it.

The problem with the static test is that the longer you leave the load on, the greater the deflection you get, due to the visco-elastic behaviour of wood, leaving you with a decision as to when to take the reading. As others have said, if the panel is not exactly flat or exactly rectangular, you also introduce some errors. Really, the only reason to use the deflection method is if there is no other way of estimating the elastic moduli, e.g. on irregular shaped panels when only a small section can be made rectangular (panels with corners missing , etc..)

Without doubt the best way is to use dynamic testing, which automatically tests deflection in both directions as it vibrates, and most closely represents the way a guitar works to produce sound (i.e. it vibrates and the frequency of modes is what we are interested in, in high performance guitars). It also takes less time to do and uses very little workshop real estate. The dynamic result is usually slightly higher than the static result, due to the visco-elastic effects which make wood appear stiffer. The extreme of this is when ultrasonic testing is utilised, which gives significantly higher results.

I have tested PRT sonically "certified" wood and on the whole my results have matched PRT's pretty closely.

[johnparchem]

I hate to show my ignorance but is elastic modulus the same as Flexural modulus in this use or is just closely related? Trevor when you mention visco-elastic behaviour of wood, I am inferring that you are describing why a flexural modulus test diverges from elastic modulus test while testing wood plates.

[Trevor Gore]

...is elastic modulus the same as Flexural modulus in this use or is just closely related?

Flexural modulus and elastic modulus tend to be the same in isotropic materials at small deflections. For larger deflections, as typical of bending tests, and non-isotropic materials (like wood) they tend to diverge.

...when you mention visco-elastic behaviour of wood, I am inferring that you are describing why a flexural modulus test diverges from elastic modulus test while testing wood plates

Correct.

[GregHolmberg]

John, Trevor--

I was unclear on what the difference is between elastic modulus and flexural modulus, so I looked it up on wikipedia.

Elastic Modulus

Flexural Modulus

According to the above, elastic modulus is a more general term, defined as stress/strain, which in an anisotropic material such as wood, has multiple values in the various directions (radial, tangential, longitudinal).

There are several ways to measure elastic modulus: Young's, shear, bulk, flexural.

Young's is about tension and compression vs. change in length.

Shear is about opposing offset forces and change perpendicular.

Bulk is about volume change from forces in all directions (opposite of compressibility).

Flexural is about flex due to a moment, typically measured by a three-point bending test of a beam (as shown below).

And then we can say that for small strains in isotropic materials, the flexural modulus is equivalent to the Young's modulus. But for wood, these would be different.

Is my understanding correct?

For a guitar soundboard, I guess we would care more about bending than tension/compression? This is what the wood-database reports (MOE).

Greg

[NRMiller1958]

It is possible to get comparative results, but you have to be very careful about how you do it.

The problem with the static test is that the longer you leave the load on, the greater the deflection you get, due to the visco-elastic behaviour of wood, leaving you with a decision as to when to take the reading.

I dealt with this phenomenon (though I didn't have a word to name it!) by loading the weight, removing it, then re-zeroing before taking a final reading. Pre-loading with a small weight that remains during the deflection measurement probably would have been a better solution.

I build archtop mandolins, so I was looking for a method that works on irregularly-shaped blocks. The biggest challenge is when they're wedge-shaped in cross section. Is there an appropriate way to use dynamic testing for such material?

[Trevor Gore]

Is there an appropriate way to use dynamic testing for such material?

The good news is "Yes there is!" I once came across a formula on the web which gave the resonant frequency of trapezoidal section panels. The bad news is I have never been able to find that formula since!

However, a regular trapezoid is basically an isosceles triangle with the top cut off (see page 4-36 of Design Ed 3 [probably the same page number in earlier editions]). So using the parallel axis theorem, you should be able to work out the second moment of area for the whole triangle and subtract from it the second moment of area of the missing "top" triangle, yielding a value of I for the trapezoidal section. Then use that value of I in Equ. 4.4-3. It's a bit of an approximation, because you are assuming a beam, not a panel, but it may be accurate enough for mandolin sized panels.

And no, I'm not going to work it out for you!!

Please let us know how you go!