I tried removing the constraints and applied force and was able to get close to the same frequencies for the butterfly modes as the simple model. By also removing the interior cylinder from our model I was able to restore the butterfly modes as well. I can see why removing the constraints and forces would make a difference, but I don't understand how the interior region which was only used to aid in making the meshing in the central region more dense would have such a strong effect. With that removed as well, we get the following results using a finer mesh (plot attached):
ratioR Lowest Drumhead mode (Hz) Lowest Butterfly mode (Hz) Any lower modes (Hz)
0.1 8777.8 7253.3 3059.7
0.3 5636.9 7264.7 4202.3
0.5 6068.5 7308.0 5980.9
0.75 7341.5 7183.0 no
1 8110.2 5951.3 no
1.1 7302.8 5308.8 no
1.3 5744.3 4087.9 no
This data is more in line with what we would expect, and indicates that the optimal region is probably between ratioR=0.6 and ratioR=0.8. I will run the looping script we designed to map out how Umax changes when varying ratioR, particularly in this interesting region.
This line was used to generate the plot from data.
figure(1); plot(ratio,drum); hold on; plot(ratio,butterfly,'rs'); plot(ratio(1:3),others,'g'); hleg1=legend('Drumhead','Butterfly','Other'); title('Eigenfrequencies of mode types for different ratioR values'); xlabel('ratioR'); ylabel('lowest eigenfrequency'); shg;
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I attempted to run the Matlab code built last week, but received an error that the mesh failed to generate on the inner domain/failed to respect edge element on geometry edge. The error occurred on the second computation with ratioR=0.2, but for ratioR=0.1 the simulation completed successfully. I reproduced the error in COMSOL and noted that for meshes with size at least as course as "course" or extremely fine, a mesh could be constructed, but for sizes in between an error was returned. This region of sizes which throw errors varies for different values of ratioR. By specifying an edge selection of the central line running down the frustum and another along the top edge of the inner cylinder and meshing points on those edges first the rest of the meshing is forced to use those nodes as a seed.
I also noted our COMSOL model had an error: ratioR was applied to the wrong face. This was corrected as was the .m file.
I added an eigenfrequency study and ran it for several values of ratioR, obtaining the following:
ratioR Lowest Drumhead mode (Hz) Lowest Butterfly mode (Hz)
0.1 3624.8 3802.4
0.3 4375.9 3785.4
0.5 4366.5 3650.0
.75 3709.0 3041.85
1 3000 2186.3
1.1 2736.2 1893.0
1.3 2247.6 1426.4
The mirror's front face is 0.17 [m]. Its Gaussian beam size is 0.0156 [m]. Its height is given by 0.01734[m^3]/(R^2*(1+ratioR+ratioR^2)) such that when the two faces have the same radii it is 0.2 [m] long.

When we talked today, I thought that these frequencies were a little low, so I ran a really simple COMSOL model of a cylinder with radius 0.17 m and height 0.2 m (attached).
I solved for the first 10 modes (the first 6 being trivial), and the frequencies I got are listed below:
Mode # Freq [Hz] Type
7 5950 Butterfly
8 5950 Butterfly
9 8106 Drumhead
10 8226 Shear
These are more in the frequency range that I expected.
**What material are you using? I used fused silica.
**I used 'finer' meshing. Perhaps your more complicated meshing is screwing with the solutions, although I'd expect it to make it stiffer, not softer.
**Are you applying force during the eigenvalue calculation? That might make it softer.
**Perhaps some of your constraints are moving the modes around. My model has zero constraints: it's just a cylinder floating in space.
Lets talk about this tomorrow.

