Paul,
I can't say I'm following everything that well. But do you need to identify productive modes? Won't that come out of the rest of the math?
Eric
When comparing plates for assessment of thick or thin, I think you should calculate the ratio of wavelength to thickness at the frequency of interest. Plywood is thinner, but its also stiffer, so will have a smaller wavelength than EPS at any given frequency. If the thickness is ~0.1 lambda, you could get away with a thin model I suppose.
Not sure what you mean by 'come out of the rest of the math'? It would certainly come out if we were (eg) doing a Helmholtz or BEM simulation, if that's what you mean. But we are not set up for that yet, and its very expensive in CPU time, and Im not sure if it would tell us a whole lot more.
The modal results by themselves can maybe be used for a rough comparison, I think. Christian has simply calculated the average value of the mode shape, which is non-zero for productive modes and close to zero for unproductive. This is a bit like the Rayleigh integral applied from infinite distance, where all parts of the panel are equidistant from the observation point. But for more complex mode shapes, the spatial distribution of the antinodes may have a significant effect upon its productivity. The other bits are interesting too - does the excitation point make a significant difference to some unproductive modes? Does the modal mass term make any difference, or does it just end up as a constant as for the simple geometry?
What I'm after right now is a good-enough proxy to get an estimate of how much each mode contributes to the SPL. I'm particularly interested as to whether asymmetrical geometries gives more productive modes. I dare to hope for this because a mode shape which cancels exactly and is unproductive in a highly symmetrical configuration like a rectangle may no longer do so when the panel is asymmetrical. Maybe the productivity is spread out more between different mode shapes?
I may try a simple average in the next few days to get an idea.
Yep, I agree, the wavelength become the effective "length", so thickness to wavelength would be the meaningful measure.
Eric
Haha, not exactly sure myself. But I guess what I mean is that if the Rayleigh integral adds up the contributions from every point on the panel, won't the contributions (for a particular mode) over the whole panel add up to near zero for a mode that's unproductive? Hence, it would automatically come out that way. I acknowledge I don't quite have a grasp on the strategy, so don't mind me if I'm mistaken. Just carry on!
Eric
Eric said: (there was no reply button available, maybe Im too early to respond?)
Yes exactly. I think the confusion was that you thought I was talking about two different things. When I mentioned about productive/unproductive modes I was merely summarising the utility and intent of calculating the Rayleigh integral numerically, not some different approach. So indeed, we would expect it to 'come out of the math'!
Yes exactly. I think the confusion was that you thought I was talking about two different things. When I mentioned about productive/unproductive modes I was merely summarising the utility and intent of calculating the Rayleigh integral numerically, not some different approach. So indeed, we would expect it to 'come out of the math'!
A more detailed look of the equations of #170 is necessary for a good implementation. Rearrangement of the equations might shows some criteria about the modes. It might be a tool to at least avoid heavy computation loads.
I tried to read the paper above, and an earlier one. Lots of unexplained math from other sources, and algorithms that are not described in nearly enough detail. I think we need a reference from a textbook.
With regard to the velocity term, I was thinking to sum over just one mode shape at a time, and get separate numbers for each one. It doesn't even matter that much whether they refer to any absolute quantity, I guess we can compare to a 'known' reference like the 1,1 mode of a rectangle. Xie and Thomson are calculating an average efficiency so are summing over all modes (which I don't really understand, because modes would be cancelling each other out in a sense within that sum, and yet each mode will resonate separately at its own frequency.
You are correct Christian in your comment about the negative value of Umn representing a phase change. I do remember that there is a 180 phase shift at resonance, so it does make sense.
These formulae come from rather advanced math, so we may end up with something meaningless unless we find a good how-to reference, or use an existing tool like BEM with a good example. There are a few variants on these methods, which I don't understand, to do with proper convergence of the integral, and efficiency. I suspect that our case is about as simple as its possible to get, just one side of a 2d surface, so some of the problems of convergence probably don't apply.
Eric, can you continue on to an harmonic analysis with Lisa? If so, does it output the velocity field over the surface?
With regard to the velocity term, I was thinking to sum over just one mode shape at a time, and get separate numbers for each one. It doesn't even matter that much whether they refer to any absolute quantity, I guess we can compare to a 'known' reference like the 1,1 mode of a rectangle. Xie and Thomson are calculating an average efficiency so are summing over all modes (which I don't really understand, because modes would be cancelling each other out in a sense within that sum, and yet each mode will resonate separately at its own frequency.
You are correct Christian in your comment about the negative value of Umn representing a phase change. I do remember that there is a 180 phase shift at resonance, so it does make sense.
These formulae come from rather advanced math, so we may end up with something meaningless unless we find a good how-to reference, or use an existing tool like BEM with a good example. There are a few variants on these methods, which I don't understand, to do with proper convergence of the integral, and efficiency. I suspect that our case is about as simple as its possible to get, just one side of a 2d surface, so some of the problems of convergence probably don't apply.
Eric, can you continue on to an harmonic analysis with Lisa? If so, does it output the velocity field over the surface?
Strange, but the "quote" option seems to be missing lately from the most recent post. I think you noticed this too Paul.
Anyway, I'm not sure what you mean by "continue on to a harmonic analysis". The only other relevant analysis method is Dynamic Response, which sounds interesting but I have not tried it yet.
Eric
Anyway, I'm not sure what you mean by "continue on to a harmonic analysis". The only other relevant analysis method is Dynamic Response, which sounds interesting but I have not tried it yet.
Eric
Attachments
Yes I noticed the missing quote button. It used to be called reply I think, so they have done some work on it and there is a but I suppose.
Yes I think dynamic response is the same thing as harmonic analysis, or frequency response analysis. A sinusoidal force is applied at a particular frequency.
To get this in Elmer I think I have to build a 3d mesh using the more general elastic model. I suspect that the dynamic response is doing something similar to the formulas, adding contributions from modes near to the frequency. I might ask on the forum.
Yes I think dynamic response is the same thing as harmonic analysis, or frequency response analysis. A sinusoidal force is applied at a particular frequency.
To get this in Elmer I think I have to build a 3d mesh using the more general elastic model. I suspect that the dynamic response is doing something similar to the formulas, adding contributions from modes near to the frequency. I might ask on the forum.
Asked on the elmer forum several questions about plate solver. Looks like it can do everything we need. I'm out on a trip atm but will try the harmonic analysis when I return.
See here https://www.elmerfem.org/forum/viewtopic.php?p=27813#p27813
See here https://www.elmerfem.org/forum/viewtopic.php?p=27813#p27813
Eric,
I found some info on how Elmer handles anisotropic materials. You have to input a matrix (or rather, a tensor) of values, either 3x3 or 6x6. You can also rotate the material axes relative to the coordinate frame. Successful use of it by a someone using it for the first time is described here https://www.elmerfem.org/forum/viewtopic.php?p=20232&hilit=orthotropic#p20232
I dont know whether the plate solver works with the full tensor (I know the general elastic model does), but I think its worth a try. I know you have done quite a bit on orthotropic materials, so if you can formulate a 3x3 tensor, I can try to plug it in and see if it works at all, and if the results are the same.
Paul
I found some info on how Elmer handles anisotropic materials. You have to input a matrix (or rather, a tensor) of values, either 3x3 or 6x6. You can also rotate the material axes relative to the coordinate frame. Successful use of it by a someone using it for the first time is described here https://www.elmerfem.org/forum/viewtopic.php?p=20232&hilit=orthotropic#p20232
I dont know whether the plate solver works with the full tensor (I know the general elastic model does), but I think its worth a try. I know you have done quite a bit on orthotropic materials, so if you can formulate a 3x3 tensor, I can try to plug it in and see if it works at all, and if the results are the same.
Paul
PS, as the post I linked above says, apparently for orthtropic input the youngs modulus value is specified as the inverse of the stiffness tensor:
I dont know if the plate solver will accept this 6x6 value, I would guess that being a 2D model its a simpler 3x3 tensor as described here: https://engineering.stackexchange.com/questions/17099/stiffness-tensor-in-two-dimensions
Anyhow, I have some hope now that the plate solver does accept orthotropic input, because the manual describes how perforated plates can be modelled by formulating an equivalent orthotropic plate.
Paul
I dont know if the plate solver will accept this 6x6 value, I would guess that being a 2D model its a simpler 3x3 tensor as described here: https://engineering.stackexchange.com/questions/17099/stiffness-tensor-in-two-dimensions
Anyhow, I have some hope now that the plate solver does accept orthotropic input, because the manual describes how perforated plates can be modelled by formulating an equivalent orthotropic plate.
Paul
Just for the pleasure to share I fixed a small bug in the FDM script so I am at the end of the current test sequence : the results in different combinations (5 exactly) of simply supported or clamp edges are close enough to elmer results so I can enter in the next sequence to simulate a free edge plate.
Thank you again Paul @pway for your help starting with elmer (not finished) and you Eric @Veleric with your example in FMEA uses with Lisa.
With the progress with the "boundary conditions" thread, I have changed a bit my plan for simulation and FDM or FEM putting higher priority on the addition of element like mass, spring (exciter) or damping at the edge than orthotropic material.
Christian
Thank you again Paul @pway for your help starting with elmer (not finished) and you Eric @Veleric with your example in FMEA uses with Lisa.
With the progress with the "boundary conditions" thread, I have changed a bit my plan for simulation and FDM or FEM putting higher priority on the addition of element like mass, spring (exciter) or damping at the edge than orthotropic material.
Christian
Paul,
I'm glad you found out that Elmer can handle orthotropic materials.
One thing that's good to realize also is that the complicance matrix is symmetrical.
So that means there are fewer independant properties than it appears.
For the 2d case (3x3) there are only 4 independant constants, not 5. if you know E11, E22 and nu12, then nu21=E22*nu12/E11.
For the 3d case (9x9) there are only 9, not 12 for the same reason.
Interestingly, the LISA shell model (and probably the Elmer plate model also) is kind of quasi-3D. That is, it requires the expected four parameters for 2D:
E11, E22, nu12, and G12,
but also requires G13 and G23. I was always surprised that it asked for these additional parameters, because I previously assumed it was a purely 2D model. But now I think it uses the "extra" G values to model the Mindlin thick plate effects.
I have noticed in the past that the eigenfrequencies predicted seem to be very insensitive to G13 and G23. But I wonder if I wasn't looking at high enough frequencies to notice an effect. I'll have to look again.
Eric
I'm glad you found out that Elmer can handle orthotropic materials.
One thing that's good to realize also is that the complicance matrix is symmetrical.
So that means there are fewer independant properties than it appears.
For the 2d case (3x3) there are only 4 independant constants, not 5. if you know E11, E22 and nu12, then nu21=E22*nu12/E11.
For the 3d case (9x9) there are only 9, not 12 for the same reason.
Interestingly, the LISA shell model (and probably the Elmer plate model also) is kind of quasi-3D. That is, it requires the expected four parameters for 2D:
E11, E22, nu12, and G12,
but also requires G13 and G23. I was always surprised that it asked for these additional parameters, because I previously assumed it was a purely 2D model. But now I think it uses the "extra" G values to model the Mindlin thick plate effects.
I have noticed in the past that the eigenfrequencies predicted seem to be very insensitive to G13 and G23. But I wonder if I wasn't looking at high enough frequencies to notice an effect. I'll have to look again.
Eric