harzer99,
Nice to see someone else finally using FEA!
As far as deteriming which mode corresponds to which peak, it's really not too hard using the tapping method. When you use the exciter at the 3/5 position, you excite a lot of modes. That's generally a good thing (for a speaker), but it doesn't help you relate the resonant frequencies with their corresponding modes.
By tapping (and micing) at particular locations, you can usually tell pretty easily which frequency corresponds to which mode. This, of course, is because you can tap at particular locations that excite a particular set of modes, and don't excite other particular modes. You could theoretically do the same with an exciter, but simply tapping at various postions is much easier. Secondly, every time you move the exciter, you create a slightly different plate with a slightly different set of modal frequencies.
My method of determing the frequencies of the first several modes of a plate is outline in this post:
https://www.diyaudio.com/community/...ll-range-speaker.272576/page-246#post-6965768
Normally, I apply those steps on a panel alone (without exciter or supports, except for two strings). First I identify the frequencies corresponding to the lowest torsional mode and the lowest bending modes in each of the two directions Then I can estimate the elastic properties of the panel using my finite element model by simply adjusting the elastic properties until the modal frequencies estimated by the model match the modal frequencies that I measured in the tap test.
Once I have the model results matching the experimental results for those three modes/frequencies, I try to validate the model further by exciting a few of the higher modes to be sure that those also match what the model predicts. Usually, I find that I can validate something like 6 to 10 modes at least.
You can also do the tap test on a plate that has the exciter already attached, but that's kind of tricky, because the exciter itself will shift the frequencies. Usually, I like to characterize the plate alone first, then add the exciter and see how far the frequencies have shifter. On plywood panels, the exciter has minimal effect, but on PS foam panels it can be pretty significant.
I'm eager to see more of your modelling and tapping results!
Eric
Harzer99,
Is Inventor able to do modal analysis for materials with different elastic properties in different directions (i.e. orthotropic materials)?
Virtually everything we typically use for panels is orthotropic (not isotropic).
I'm particularly interested because I expect to have Inventor Pro shortly. My (old) version of Inventor was Inventor LT (now discontinued), but it did not have FEA capability.
Eric
Is Inventor able to do modal analysis for materials with different elastic properties in different directions (i.e. orthotropic materials)?
Virtually everything we typically use for panels is orthotropic (not isotropic).
I'm particularly interested because I expect to have Inventor Pro shortly. My (old) version of Inventor was Inventor LT (now discontinued), but it did not have FEA capability.
Eric
Hi Eric,
I have seen the option in the materials for it but I'm not entirely sure if only applies to static load analysis. For better mode/ dynamic analysis you should check out Inventor Nastran it is a lot more sophisticated then Inventor Pro in terms of dynamic simulations but as everything with Autodesk very expensive. I wonder which solution most of the papers use. Some will definetly have a custom solution with FE solvers like Fenics.
Also my real name is Leonard
Hi Christian,
do you mean having the speaker suspended by surrounding foam? I'm looking forward to figuring out an explanation why this is boosting lower frequencies.
I noticed that at short distances the bass is so strong you can really feel it with your hand, that effect dies off really quickly. I don't have too much experience with Subwoofers in general but my hunch is it dies off faster than with normal speakers. This would implicate some cancellation at distance.
What does FR mean? My audio terminology is quite limited.
Leonard
Leonard,
FR is simply frequency response, as in a graph of sound power level as a function of frequency.
You are exactly right about the bass effect falling off quickly with distance. It is because of the effect demonstrated here:
https://www.acs.psu.edu/drussell/Demos/EvanescentWaves/EvanescentWaves.html
At lower frequencies (where the speed of the bending wave in the plate is slower than the speed of sound in air), the acoustic waves imparted to the air are so called "evanescent" waves, which decay exponentially with distance. The frequency above which the acoustic radiation is no longer "evanescent" is called the "coincidence frequency" and is a function of the plate stiffness and density. The stiffer and lighter the plate, the lower it's coincidence frequency.
fc is coincidence frequency, c0 is the speed of sound in air, mu is the areal density of the panel and B is the bending stiffness of the panel.
Incidentally, I believe that the coincidence frequency is also the frequency at which the wavelength in air is the same as the wavelength in the panel (which you mentioned in your earlier post). But most usually the effect is written about in terms of the wave speed rather than wavelength.
From the link above:
Plate Wave Speed (Trace Velocity) Slower than Sound Speed in Fluid
As the speed of the transverse bending wave in the plate decreases and approaches the speed of sound in the fluid, the direction of the radiated plane wave rotates from upward, perpendicular to the plate surface, to being parallel to the plate surface, when the two speeds are exactly the same. The condition when the flexural bending wave speed in the plate equals the speed of sound in the fluid is called "coincidence" since the two wave speeds "coincide". When the speed of the flexural bending wave in the plate is slower than the speed of sound in the fluid, the plane wave cannot bend back toward the plate surface, but instead the wave becomes evanescent with the wave amplitude decaying exponentially in the vertical direction away from the plate surface. Particles in the fluid near the plate surface move in counter-clockwise ellipses as the flexural wave passes by, while particles far from the plate surface don't move at all.Eric
@harzer99
Hello Leonard
Yes FR for Frequency Response. Sorry for the use of an abbreviation.
You will find different examples of foam suspensions in the realization of DML generally made of some double face foam tape or some foam used to seal doors or windows against cold air. I have used a 17x17mm one all around my plywood DML. I guess it gives a panel mounting between free edges (that is approached with some strings) and clamped.
Some months ago, I compared (just by measurements) a free panel (no suspension) and a foam suspended one (same material, same dimensions) : the foam suspended one had nicer low frequency roll off.
I don't think we can say it boots the bass.
Please find attached a file I try to maintain that gives links to post in the may DML thread. Among them, frequency responses Eric posted with different suspension methods.
Christian
Hello Leonard
Yes FR for Frequency Response. Sorry for the use of an abbreviation.
You will find different examples of foam suspensions in the realization of DML generally made of some double face foam tape or some foam used to seal doors or windows against cold air. I have used a 17x17mm one all around my plywood DML. I guess it gives a panel mounting between free edges (that is approached with some strings) and clamped.
Some months ago, I compared (just by measurements) a free panel (no suspension) and a foam suspended one (same material, same dimensions) : the foam suspended one had nicer low frequency roll off.
I don't think we can say it boots the bass.
Please find attached a file I try to maintain that gives links to post in the may DML thread. Among them, frequency responses Eric posted with different suspension methods.
Christian
Here is the way I typically use to determine the elastic properties of bending wave plate materials using the "tap test" method.
The following assumes that you have and know how to use REW, and also have a Finite Element Modelling (FEM) program that you know how to use. I use LISA, but there are many others. It's not actually necessary to have the FEM program, but it makes it easier, and for simplicity, the following assumes that you have an FEM program.
Also it a assumes that you have a rectangular plate of the material you want to assess that is appropriately sized. Typically dimensions in the range of 300 to 600 mm for each the length and width work fine. The panel can be square, unless the material is actually isotropic (or close to it), in which case square can give confusing results. I usually use a roughly 400 mm x 580 mm panel, but that's an arbitrary choice, other sizes can work just as well. The only thing to be careful of is to avoid a very large panel. With a very large panel, the lowest resonances can be too low to accurately determine using REW. I usually prefer it if the lowest resonances are above 40 Hz.
The panel thickness is whatever it is, but the results will be the most accurate if the thickness is less than about 1/50th of the shorter dimension of the panel.
This procedure is based on the assumption that the plate material is orthotropic. That is, that the elastic moduli across the length and width are different. For an orthotropic plate, there are actually six independent elastic properties: E1, E2, G12, G13, G23 and Nu12. The methodology I will describe determines only the first three of these. However, these three are enough to model bending waves well. There are some additional steps you can take (which I hope to describe in another post) to determine Nu12, if you want a slightly better model. Bending wave frequencies are very insensitive to the the other two shear moduli (G13 and G23), so there is no way to deduce them from these tests (nor any value in doing so), as far as I know. Typically I just keep all three shear moduli as the same number.
Basically, the method consists of identifying the frequencies of three particular modes, and using those frequencies to determine E1, E2 and G12.
Here are the steps:
Set Up FEM Model
1. Measure the length, width, thickness and weight of your plate as accurately as possible. Use these to determine the density of your plate.
2. Create an FEM model of your plate with the measured dimensions, density, and "free" boundary conditions.
3. Make an educated guess for the elastic properties. It doesn't have to be a good guess, but starting with something in the right ballpark is better. For a plywood plate I might guess:
Identify the Actual Modal Frequencies
Determining the Elastic Constants
Eric
The following assumes that you have and know how to use REW, and also have a Finite Element Modelling (FEM) program that you know how to use. I use LISA, but there are many others. It's not actually necessary to have the FEM program, but it makes it easier, and for simplicity, the following assumes that you have an FEM program.
Also it a assumes that you have a rectangular plate of the material you want to assess that is appropriately sized. Typically dimensions in the range of 300 to 600 mm for each the length and width work fine. The panel can be square, unless the material is actually isotropic (or close to it), in which case square can give confusing results. I usually use a roughly 400 mm x 580 mm panel, but that's an arbitrary choice, other sizes can work just as well. The only thing to be careful of is to avoid a very large panel. With a very large panel, the lowest resonances can be too low to accurately determine using REW. I usually prefer it if the lowest resonances are above 40 Hz.
The panel thickness is whatever it is, but the results will be the most accurate if the thickness is less than about 1/50th of the shorter dimension of the panel.
This procedure is based on the assumption that the plate material is orthotropic. That is, that the elastic moduli across the length and width are different. For an orthotropic plate, there are actually six independent elastic properties: E1, E2, G12, G13, G23 and Nu12. The methodology I will describe determines only the first three of these. However, these three are enough to model bending waves well. There are some additional steps you can take (which I hope to describe in another post) to determine Nu12, if you want a slightly better model. Bending wave frequencies are very insensitive to the the other two shear moduli (G13 and G23), so there is no way to deduce them from these tests (nor any value in doing so), as far as I know. Typically I just keep all three shear moduli as the same number.
Basically, the method consists of identifying the frequencies of three particular modes, and using those frequencies to determine E1, E2 and G12.
Here are the steps:
Set Up FEM Model
1. Measure the length, width, thickness and weight of your plate as accurately as possible. Use these to determine the density of your plate.
2. Create an FEM model of your plate with the measured dimensions, density, and "free" boundary conditions.
3. Make an educated guess for the elastic properties. It doesn't have to be a good guess, but starting with something in the right ballpark is better. For a plywood plate I might guess:
- E1, E2 = 5 GPa
- G12, G13, G23 =1 GPa
- Nu12=0.2
Identify the Actual Modal Frequencies
- First, you want to identify the frequency of the first of the three modes pictured, the shear mode. Hang the panel vertically from the center of the long side and the short side, that is, where the blue nodal lines in the first mode above meet the edge of the panel. I have wires hanging from the ceiling with alligator clips on the ends, but you can use tape or anything else that is sufficiently strong to hold the panel.
- Position your microphone very close (within 10 mm or so) to any corner of the panel.
- Open RTA mode of REW, and choose Spectrum mode/No Averaging/8 Averages. Start the RTA.
- Tap any corner of the panel. (My "tapper" is a stick with a wooden ball on one end and a rubber ball on the other. I can use either end for tapping.) Watch the (many) peaks show up in the RTA spectrum. Pause the RTA at any instant when the peaks are sharp. The peaks rise and fall. Here we are looking for the frequency of the shear mode, which should be one of the two lowest frequency peaks.
- To positively identify the frequency of the shear mode, tap the panel in the center, and compare the new peaks to the original peaks. When tapped in the center, one of the peaks will be much smaller or possibly disappear altogether. The one that disappears with the center tap, and reappears with a corner tap, is the shear mode. Pause the RTA when the peaks are strong and use the cursor to identify the exact frequency of the shear mode.
- Next, identify the frequency of the bending mode shown in the second figure.
- Move the support wires to hang the panel from one of the long edges. Put the wires at about 0.2 x L from the panel edges. Relocate the mic to either the center of the panel or either the left or right edge. Restart the RTA and tap the panel. Look for the strongest peak. This is most likely the frequency corresponding to the bending mode of the second figure. You may also see a (likely weak) peak at the frequency corresponding to the shear mode, but ignore that one now. Confirm that the strong peak is truly corresponding to the mode shown in the second figure by tapping the panel anywhere along the blue area in the second figure. The peak that was previously very strong should become very weak or disappear when you tap the panel in the blue (nodal) region, but reappear when you tap in the center or in the center of the left and right edge (where the panel is red in the second figure). Use the cursor to identify the frequency of the first bending mode.
- Note that the location of the hanging points is intended to be at nodal points for the mode being identified. However, those nodal points can be at slightly different locations, depending on the elastic constants, so it's impossible to know exactly where the hanging points should be. So if you want to be as accurate as possible (and why not?) move the support points slightly outward and repeat step 7. Then move them slightly inward and do it again. Ideally, find the hanging location that gives the highest frequency of all such trials, as the wires reduce the frequency, unless they are located exactly at the nodes.
- Next, identify the frequency of the bending mode shown in the third figure.
- Turn the panel 90 degrees and hang the panel from one of the short edges. Put the wires at about 0.2 x W from the panel edges.
- Repeat as in steps 7 and 8 to identify the frequency of the bending mode in the third figure.
Determining the Elastic Constants
- Revise your guess for G12 in the FEM until the model prediction for the frequency of the shear mode matches the frequency you identified for the shear mode in step 5 above.
- Revise your guess for E1 (the modulus in the direction corresponding to the long direction of the panel), until it matches the frequency you found in step 8 above, corresponding to the first bending mode (mode of second figure)
- Revise your guess for E2 (the modulus in the direction corresponding to the short direction of the panel). until it matches the frequency you found in step 11 above (mode of third figure).
- Repeat 1-3 until the FEM estimates of the frequencies of the three modes match the frequencies you observed by tapping. Note that the three modes are nearly independent, so the adjustments you make to match each of the three modes will have only a small effect on the FEM model prediction of the other two modes. So the number of iterations required will be few.
- Verify that the next several natural frequencies predicted by the FEM model also show up in tap testing. For each mode predicted by the model, hang the panel from nodal regions (blue). Then place the mic in front of an antinode (red/yellow/green) region, and tap any of the antinode regions. Asstrong peak should appear in the RTA at the same frequency predicted by the model. Also, verify that no peaks occur in the tap testing, that are not consistent with the predictions of the FEM. Note that the hanging locations for each of the modes shown below can be pretty nearly the same locations as you used to find the two original bending modes.
Eric
@Veleric
Hello Eric,
Thank you for your post.
As mentioned in the post before, I already tested the tap test. At the end, the values are extracted by some formulas not by running FEM tool.
For now, I haven't really succeeded with FEM. Those tools for sure powerful are a bit obscure too me. So I started an other approach thank to FDM (Finite Difference Method) and Python scripting. Going on.. slowly.
The basis of the method is to solve the PDE (partial differential equation) of an orthotropic plate. I started a document about it (help a lot to clarify ideas)
Could you help me in clarifying what is Dxy in the above equation in relation to the characteristics you listed?
Or simply some advice of readings.
Christian
Hello Eric,
Thank you for your post.
As mentioned in the post before, I already tested the tap test. At the end, the values are extracted by some formulas not by running FEM tool.
For now, I haven't really succeeded with FEM. Those tools for sure powerful are a bit obscure too me. So I started an other approach thank to FDM (Finite Difference Method) and Python scripting. Going on.. slowly.
The basis of the method is to solve the PDE (partial differential equation) of an orthotropic plate. I started a document about it (help a lot to clarify ideas)
Could you help me in clarifying what is Dxy in the above equation in relation to the characteristics you listed?
Or simply some advice of readings.
Christian
Christian,
I'm not positive, but I'm pretty sure that Dxy is simply the shear modulus (Gxy). Or that 2*Dxy =Gxy.
Eric
Christian,
Sorry, I spoke too soon. My answer above in almost certainly wrong.
But I do think that Dxy is the "torsion" analog of the bending stiffnesses Dx and Dy. That is, where Dx or Dy is the bending stiffness, Dxy is the torsional/shear stiffness of the plate.
since D=(E*h^3)/12 , the torsional analog should have similar form, and my best guess is this:
Dxy=(G*h^3)/32. Though I must admit this is still a guess, and I am particularly uncertain about the correct value for the constant (32). I got it from the link below, but I'm not sure if that's correct in this context.
Since your equation is written with the term 2*Dxy, it might also be that 2*Dxy=(G*h^3)/32, and hence Dxy=(G*h^3)/16.
Or that might be wrong too! So helpful I am! (sorry).
https://www.engineersedge.com/calculators/torsional_stiffness_rectangular_plate_14969.htm
@pway do you know the answer?
Eric
No I don’t really know, but this book chapter has a straightforward development arriving at a similar expression on page 48. I used sci-hub to access. Their expression uses H instead of Dxy, which includes Dx, Dy and Gxy. But here may be different developments with different assumptions idk.
https://doi.org/10.1142/9789812815798_0002
Thanks for the procedure Eric, I’ll be using it when we get back to normal routine after Christmas. Plus the fem and other stuff. It’s hard to find time for everything. One of these days I hope to build some real speakers 🫤
+ @Veleric
Here is some further reading on the topic... I think it answers to my question : Theoretical Background of the “Resonalyser Procedure”
And this : Orthotropic Multiplex wooden plate
Great find Christian,
I think I saw the first link before, as it's referenced in the Wiki link I found originally.
But I never saw the second link before (the wood plate example), and that one does have your answer here:
So I was wrong after all to think D12 was related to G12. D12 is actually related directly to the poisson's ratio, not the shear modulus. It's D66 that's related to the shear modulus G12 (see the pair of relations at the bottom).
The only problem is they made a typo (I circled in red). I think what they meant to write there was:
G12=12*D66/t^3 , as it's clearly just the inverse of the equation to the left of it.
They made another mistake in the article too. They list the plate in the example as being .0015m thick, but they actually meant .015 m. Otherwise the panel density is 10 times too heavy. They have it shown correctly as .015 m in the data sheet linked at the end of the article, however.
Eric
I’m also thinking that ‘dumpster fire’ describes the other forum pretty well at this point. I wonder whether those who want to pursue a more technical approach would be more comfortable using this forum instead? There may not be a critical mass to get moving, or to keep it moving in the longer term. We all come and go as time permits.
Still, the title, while fairly specific, does connote a technical, empirical approach, so is not inappropriate. And we would not antagonise less technically-minded people.
What do you think Eric? Christian ?
Still, the title, while fairly specific, does connote a technical, empirical approach, so is not inappropriate. And we would not antagonise less technically-minded people.
What do you think Eric? Christian ?
Hello Paul,
I am currently trying to get results from a Python script using Finite Difference Method. If it gives results my idea is to split the communication about it in 2 : some general outputs in the main stream with the minimum of math, the detail if other want to use the script in a more specific thread.
Seems to be close to your feeling.
Happy New Year to all!
Christian
Happy New Year Paul and Christian,
The DML thread is a strange beast. Even ignoring the current state of affairs. Every aspect is discussed in the same thread and five or more conversations on different topics are overlapping at any given time. It's an entire forum in a single thread! Why is that??
I suspect the critical mass thing may be crux of it. The number of us interested in DMLs are in this strange middle range, where there are too few of us to sustain a conversation about a specific topic, but too many of us to be contained in a single thread.
On top of that, there is now an "expectation" that anything related to DML will be posted in this thread. Everybody posts everything in "The" DML thread. Why even bother looking elsewhere?
I actually started this particular thread, in part, as an attempt to break out of that pattern. But I also worried that no one would find it!
But has a new day dawned? With the recent addition of the exciter thread we have two focused (normal) threads active, in addition to the monster thread, Yeehaw!
All that said, feel free to post anything you want to this thread. Certainly anything related to "tapping" and "modelling" would fit as far as I'm concerned.
But also consider when it makes sense to open a new thread.
Eric
I've been playing with a script looking at modes vs aspect ratio, and I think it shows why high aspect ratios may work best.
In what follows I am using:
Here is a plot of all modes < 200 Hz.
The first 'series' of modes with n=1 looks like this:
With a high aspect ratio, the 1,1 mode is at a slightly higher frequency, dominated by the 1/b^2 term. This actually helps because it lifts the fundamental from a pretty useless low frequency up to a point where it might do some good.
More importantly, side a is much longer, so each successive mode (adding m^2/a^2) adds much less than at low aspect ratio. Consequently, more modes are squeezed in at low frequency and are evenly spaced. At low aspect ratios, that first series quickly exceeds 100 Hz.
Not only that, looking again at the first graph, the first series has 'clear air' at the higher aspect ratios, because the second series with n=2 rises steeply leaving the first series alone and presumably giving a smoother LF response.
Script attached.
In what follows I am using:
- height (long dimension) = a and width=b
- mode indices m and n for correspond to sides a and b.
- area 0.5 m^2, h = 0.015 m
- nu = 0.3 # Poisson
- E = 4.0E6
- rho = 26 # density kg/m^3
Here is a plot of all modes < 200 Hz.
The first 'series' of modes with n=1 looks like this:
With a high aspect ratio, the 1,1 mode is at a slightly higher frequency, dominated by the 1/b^2 term. This actually helps because it lifts the fundamental from a pretty useless low frequency up to a point where it might do some good.
More importantly, side a is much longer, so each successive mode (adding m^2/a^2) adds much less than at low aspect ratio. Consequently, more modes are squeezed in at low frequency and are evenly spaced. At low aspect ratios, that first series quickly exceeds 100 Hz.
Not only that, looking again at the first graph, the first series has 'clear air' at the higher aspect ratios, because the second series with n=2 rises steeply leaving the first series alone and presumably giving a smoother LF response.
Script attached.
Last edited:
Thank you Paul.
Just unzipping it, the script works on y computer. Happy to see somebody else scripting in Python!
In previous posts it was shared that only odd, odd modes produce sound, what about filtering on them?
My script based on FDM (finite difference method) is on progress; The simulation of a simply supported plate seems ok (eigenfrequencies equal to the formula prediction). I added one feature to show the mean value of the mode shapes. Only the odd, odd have a non zero mean value. Kind of confirmation. Next step is to compare results against other simple cases like clamped and then to add the free edge condition.
The interesting output of this FDM script is to get a table of the displacement of each point. I would be interested if you have an idea to get from a FEM solver embedded in a Python script.
Christian