Hello Paul,
I had a new look at the Rayleigh integral, you are right it is omega.speed so omega².displacement.
Here is an interesting site gathering almost all the physics of DML : Euphonics The science of musical instruments
Rayleigh in section 4.3.2 The Rayleigh integral and the baffled piston
Paul,
Could you post the Elmer files of this set up please. I thought to see the zip yesterday but not... probably reading too many posts
Thanks
Christian
Paul,
I just compared our 2 sets of values, they fit not too badly not to say pretty well. This is really encouraging, the exciter is in the game.
Attached. I wont be around next few days, have fun!
There is a python script I used to extract data from the vtu file, but I have modified it since posting results. You'll have to edit it. (And delete the function calculating dbA 🙂) I was using the shell_eigen.sif file.
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Eigenvalues, mode shape and modal superposition
MDOF: response using modal superposition (Lecture 7) is somebody wants a deeper understanding of the physics and math behind this topic. Lecture 3 is also a key in the understanding of the relations in the Pudra's thesis
Christian
MDOF: response using modal superposition (Lecture 7) is somebody wants a deeper understanding of the physics and math behind this topic. Lecture 3 is also a key in the understanding of the relations in the Pudra's thesis
Christian
Looks good,will watch when I get home. Only have one bar of cell phone signal here. I also found a paper on modal mass, and also read that elmer eigenmodes are normalized to unit modal mass.
Hello Paul,
If in your readings you find something making the link between modes, eigenvalues, mode shape and modal superposition it will be interesting. Modal superposition is the next step to get the speeds at any frequency. Some additional explanations aside the Putra's thesis are welcome.
Christian
I'd like to order a few of these soon.
SNR & THD are not Hi-end audio by any means. But they will prolly make enough noise to keep the punters happy.
The DSP interfaces with SigmaStudio from Analog Devices... Steep learning curve coming up...
https://tinyurl.com/DSP-Amp
Yes Ive seen these. Very convenient for your use-case. Let us know how good (or bad) the noise is when no content is playing.
You can also buy direct from Sure electronics.
You can also buy direct from Sure electronics.
Hi Christian
You will probably have seen these already, but they are good I think:
From Comsol multiphysics docs: https://www.comsol.com/multiphysics/mode-superposition.
Also the next one in the list 'response spectrum analysis'
And this one that covers modal mass in some detail, with a proposal to standardise its meaning:
https://www.hindawi.com/journals/sv/2020/8648769/
Next step for me is to add a frequency response function to my script that calls the harmonic analysis of Elmer, when I find the time. I believe that Elmer takes care of the majority of this for us - the modes are scaled to unit modal mass, mode shape at any frequency can be computed, the damping is taken care of, the sensitivity of the mode to the drive point is taken care of. Average across the eigenmode, scale properly and I think we have a frequency response.
Elmer does not use modal superposition, it does the calc from first principles.
Here's a first frequency response from harmonic analysis.
(1,3) mode at 35 Hz
(1, 5) mode at 80Hz not showing a peak - why?
(3, 1) mode at 102 Hz
(3, 3) mode 125 Hz
I have calculated the panel average using triangles rather than points - with points it's incorrect because there are obviously more points than triangles! And this will allow the Rayleigh calc including distance/phase to observation point if it proves worthwhile.
Still puzzling over the physical meaning of the complex displacement data, and whether it represents phase differences over the surface of the panel. I assumed the reference would be the applied force (the exciter) so that its movement would be at phase zero, but that does not appear to be the case. I assumed that I need to find the magnitude rather than just take the real part, but am not even sure about that.
There is quite a lot going on here that I have to look at. Looks like the phase shifts of harmonic mode lead prevent the response going very near to zero. Degenerate modes seem susceptible to deep nulls I think - not sure yet. Dont know if much other than the peaks represent a real physical effect.
(1,3) mode at 35 Hz
(1, 5) mode at 80Hz not showing a peak - why?
(3, 1) mode at 102 Hz
(3, 3) mode 125 Hz
I have calculated the panel average using triangles rather than points - with points it's incorrect because there are obviously more points than triangles! And this will allow the Rayleigh calc including distance/phase to observation point if it proves worthwhile.
Still puzzling over the physical meaning of the complex displacement data, and whether it represents phase differences over the surface of the panel. I assumed the reference would be the applied force (the exciter) so that its movement would be at phase zero, but that does not appear to be the case. I assumed that I need to find the magnitude rather than just take the real part, but am not even sure about that.
There is quite a lot going on here that I have to look at. Looks like the phase shifts of harmonic mode lead prevent the response going very near to zero. Degenerate modes seem susceptible to deep nulls I think - not sure yet. Dont know if much other than the peaks represent a real physical effect.
What I have so far replicates some aspects of the freq response, but it’s not really physically meaningful. The main integral formula with the complex exponent is the most important bit!
For example, the 3,3 mode radiates not just because there are bits left over after you integrate, but it results in corner modes. And other modes which are known to radiate such as even,odd modes will never give us any output using the simplistic average.
It has to be the full formula or Fourier transform method. Even then, it will be for a plate in an infinite baffle.
For example, the 3,3 mode radiates not just because there are bits left over after you integrate, but it results in corner modes. And other modes which are known to radiate such as even,odd modes will never give us any output using the simplistic average.
It has to be the full formula or Fourier transform method. Even then, it will be for a plate in an infinite baffle.
Hello
Just found this paper to be added in this thread.
On measuring the elastic and damping constants of orthotropic sheet materials
It is a variant of the technique proposed in this thread where the tapping method is replaced by Chladni figures of a free edge plate above a loudspeaker. The second part is about the damping coefficients. Other interest of the paper is the link to plate equations.
Christian
Just found this paper to be added in this thread.
On measuring the elastic and damping constants of orthotropic sheet materials
It is a variant of the technique proposed in this thread where the tapping method is replaced by Chladni figures of a free edge plate above a loudspeaker. The second part is about the damping coefficients. Other interest of the paper is the link to plate equations.
Christian
A couple more initial responses from a direct implementation of Rayleigh integral taking account of the additive phases of each element to the observer (microphone) position.
Density = 26
Thickness = 0.015
Tension = 0.0
Poisson ratio = 0.3
Youngs modulus = 4000000.0
Panel size 1m x 0.5 m.
Exciter pos 2/5, 2/5
The main differences I would point out today are the extra nulls just under 200 Hz, and the extra peaks over 400Hz.
The nulls are due to the particular mic location being at a spot to create a null somewhere in the spectrum. The depth of these nulls will be unaffected by damping, because they are a function of observer location. The graph above is for an observer location at (0, 0, 3) which is in front of one of the panel corners. Below is a response at a different location in 3m in front of the centre of the panel (0.25, 0.5, 3). Note how the nulls below 200Hz have shifted.
The peaks above 400Hz are edge modes I believe. Have to check this.
Ignore the fact that the overall levels are less - I was playing with damping and didnt put it back to the same value.
Code is still in a state of flux, and I will move now to shell solver, which has a better damping setup and ability to add extra masses.
I will post code when its a bit more stable. Some aspects are still puzzling, like no apparent increase in average response level with frequency. I thought I would see an increase due to omega squared, but the main one may be due to increase in radiation efficiency towards coincidence, which is not accounted for in this model.
Paul
Density = 26
Thickness = 0.015
Tension = 0.0
Poisson ratio = 0.3
Youngs modulus = 4000000.0
Panel size 1m x 0.5 m.
Exciter pos 2/5, 2/5
The main differences I would point out today are the extra nulls just under 200 Hz, and the extra peaks over 400Hz.
The nulls are due to the particular mic location being at a spot to create a null somewhere in the spectrum. The depth of these nulls will be unaffected by damping, because they are a function of observer location. The graph above is for an observer location at (0, 0, 3) which is in front of one of the panel corners. Below is a response at a different location in 3m in front of the centre of the panel (0.25, 0.5, 3). Note how the nulls below 200Hz have shifted.
The peaks above 400Hz are edge modes I believe. Have to check this.
Ignore the fact that the overall levels are less - I was playing with damping and didnt put it back to the same value.
Code is still in a state of flux, and I will move now to shell solver, which has a better damping setup and ability to add extra masses.
I will post code when its a bit more stable. Some aspects are still puzzling, like no apparent increase in average response level with frequency. I thought I would see an increase due to omega squared, but the main one may be due to increase in radiation efficiency towards coincidence, which is not accounted for in this model.
Paul
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Hello Paul,
2 proposals of elements to consider :
- Which damping into the material have you modeled? Over this range of frequency, one might think the damping is constant, so the quality factor of each mode (the width of the modes), so as the density of modes increases with frequency, the level might increased?
- The model is probably for now with a constant force (same force for each frequency considered) which is not true in the reality because the exciter is in most of the cases voltage driven (not current driven) so there is a kind of self regulation that limits SPL at the peaks. Below a tentative of illustration/explanation. it is a trial of measurement I made by the end of the year to see the current that flows in the exciter (here a simple sheet of 20x30cm XPS). The current was measured as the voltage across a 0.47Ohm resistor in series with the exciter. I had too noise in the measure to be fully satisfied but it is ok for our point. What we see as expected in a voltage driven exciter is a reduction of the current at each modes (not only the productive ones). As the force F = Bl.I, Bl being the force factor, F is reduced at each resonance. The reduction decreases when the frequency of the mode increases (can't explain why!). This due to the effect of the mechanical impedance which reaches a local minimum at each mode and is "visible" in electrical side as a maximum and is important compare to the DC resistance (5 to 10 times the DC resistance here?)
The vertical scale is log. I would have prefer lin but I was not able to do it at the moment!
The impedance measurement of the exciter and of the panel is something I intent to develop. 2 reasons : the poor data about the exciters to get voice coil mass, spider compliance and so one and to see what we can learn about the damping of the panel (at each resonance, the amplitude is made from the damping).
Out of the scope of our topic, I wonder if the coincidence frequency is visible on this kind of measurement?
Christian
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@pway
Hello again Paul.
I did some impedance measurements today. See #9456 in the main thread for the exciter impedance (free air and mass added).
Below is the impedance with a 20x30 XPS 9mm plate.
The very sharp spikes are from some set up problem I haven't identified it (REW compatibility with linux or Linux with my soundcard or some interference because of power supplies?).
Except that, you can see the effect of the mechanical impedance at resonances. This time the vertical axis is correct in Ohm (I went through the calibration).
The peaks are from 45Ohms to about 10Ohms up to 1kHz. So in this example (ok this not an operational DML), it divides the current so the force by 2 to 5 at the resonances.
I would like to find the cause of the sharp spikes... but the set up seems correct. I have at hand a second unused exciter to evaluate their dispersion and a pair of canvas panels. For this week I am away from my plywood panels.
Christian
Hello again Paul.
I did some impedance measurements today. See #9456 in the main thread for the exciter impedance (free air and mass added).
Below is the impedance with a 20x30 XPS 9mm plate.
The very sharp spikes are from some set up problem I haven't identified it (REW compatibility with linux or Linux with my soundcard or some interference because of power supplies?).
Except that, you can see the effect of the mechanical impedance at resonances. This time the vertical axis is correct in Ohm (I went through the calibration).
The peaks are from 45Ohms to about 10Ohms up to 1kHz. So in this example (ok this not an operational DML), it divides the current so the force by 2 to 5 at the resonances.
I would like to find the cause of the sharp spikes... but the set up seems correct. I have at hand a second unused exciter to evaluate their dispersion and a pair of canvas panels. For this week I am away from my plywood panels.
Christian
Christian,
Nice measurement. Do you have some correlation with tapping or modeling that confirms the modes at the same frequencies as the dips in the current flow test? It seems certain that they must be, but it would be great to confirm.
Also, clearly some dips in the current are deep and others shallow. Any correlation of deep vs. shallow with the mode type? Or exciter position relative to the mode (close or far from antinode, for example)?
Eric
I seems to be viscous (velocity-proportional) damping with the plate model. Does not seem to have much effect on anything but the peak height. But I dont get velocity from the model itself but calculate as proportional to displacement as we discussed. So viscous damping probably does not work properly. For shell model, mass-proportional damping is available.
Density of modes is about constant with frequency, but increases of course with log f. So yes we can expect an increase due to that if I were to go much higher in freq.
Yes, constant force is the model.
The increase resistance you are measuring would be due to back-emf I suppose.
Odd multiples of 50Hz. Looks like a square wave at mains frequency. Are you working near a motor? Air con, refrigerator etc? Or an SCR LED light dimmer?
Paul
It interesting that the basic frequency response level seems to have a 'baseline' around (around 60dB in the plots I gave). I suspect this may be a real effect. See in my post #271 how the respoinse levels off at 50, 200, 400, despite there being even modes in those regions.
My theory is that even-even or even-odd modes dont average to exactly zero, because the regular changes in phase over the panel surface give an average bias to the sum. But when there is a degenerate mode, the two resulting panel modes are randomised, and remove the bias, giving a much deeper null. That's my working theory anyhow.
My theory is that even-even or even-odd modes dont average to exactly zero, because the regular changes in phase over the panel surface give an average bias to the sum. But when there is a degenerate mode, the two resulting panel modes are randomised, and remove the bias, giving a much deeper null. That's my working theory anyhow.