I used COMSOL with MATLAB to run the simulation. I tried to vary support position and checked the mirror displacement along the beam line axis and tilt angle.
With Aidan help, I am finally able to run matlab with comsol to get the results (displacement of the mirror surface and tilt).
We are not planning to cut the cavities for support points, so we will choose the support positions on the spacer's surface, with parameter X and theta, see the figure below for their definitions.
As a start, I chose theta = 30 and 60 degree. The displacement and tilt (due to cavity sagging under its weight at 1g)as a function of support position are plotted below.
It is possible to minimize the tllt, but the displacement is still a bit bad. The result from 8" spacer, the sensitivity to acceleration is (dL/L) / (m/s^2) = 2x10^-10, while the current result will be about 1x10^-10. Since the cavity is shorten by ~ a factor 4, I expect a better sensitivity to vibration.
==next==
I'll try to change the area of the support points to check its effect on the displacment.
I have to check if I can constrain the support points in one direction or not.
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I'm still working on COMSOL, now my model has the following features:
- support points are simulated by four rectangles on the spacer surface. The support areas can be changed, and their positions can be moved along the beamline and around the cross section directions. I'm still not sure what should be the effective area for the simulation. However, the paper from Milo's group [2009] showed that the areas of the supports points do not affect the optimum position that much (but the support must be constrained in the same direction as gravity only). I have not tried to constrained the points in only one direction yet.
- I used a symmetry plane to model only half of the spacer. This will reduce some simulation time and avoid any asymmetry due to the mesh size.
- I'm trying to use matlab with comsol and print out the result. The work is stil in progress.
Note:
Milo etal. 2009 Phys Rev A 79.053829.
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