aLIGO Suspensions Toy Model

Response to question in: Disscussion of the code of a 'comsol with matlab' model file (partially complete).

trange = ['range(0,' num2str(dt) ',' num2str(t_end) ')'];

The above line converts the quatity 'dt' and 't_end' to a string and concatenates it along with the rest of the string to make a valid string that would be understood by COMSOL.

You'll notice that the range command that is given to COMSOL is in single quotes, that means that all Matlab is doing is feeding to COMSOL a string, just as you would send it numerical values as a string.

It is COMSOL that evaluates this range command, so it can be different from Matlab's range command.

Tue Jun 11 10:21:05 2013

Re: Disscussion of the code of a 'comsol with matlab' model file

Quote:

that compute the analytical solution or the COMSOL simulations.

>The part of the code ( the second if...end block) in "Main_thermo_refracive.m" that calls the COMSOL simulations, calls the function "thermo_refractive_COMSOL_1D_axisymmetric".

>In this function, the parameters are extracted from the structure 'param' and stored in separate variables. The time step in the simulation, the end time, mirror radius are defined and the function

that generates the model "thermo_refractive_COMSOL_1D_axisymmetric_model" is called which prepares the model in COMSOL.

> it should be noted that it is much of much ease to the user to define a simple model in COMSOL and export it in Matlab and then analyzed the same.

I had created a simple such file which a simple 3D metal bar is created and added some physics and study to see how the matlab file.

>The first thing done by the model builiding function is that it extracts a few parameters and stores them in separate variables in the first lines

f_mod = param.COMSOL.simulation_modulation_freq;
dt = param.COMSOL.simulation_time_step;
t_end = param.COMSOL.simulation_end_time;

>Since COMSOL accepts string arguments, the time steps are defined as a string

trange = ['range(0,' num2str(dt) ',' num2str(t_end) ')'];

The above line converts the quantity 'dt' and 't_end' to a string and concatenates it along with the rest of the string to make a valid string that would be understood by COMSOL.

>The COMSOL class is called next by the following two import statements (after a series of displays on the screen showing the status of the simulation).

model = ModelUtil.create('Model');

>The above statement created an object called 'model' in Matlab and and a model in COMSOL by the name of 'Model'. The various attributes of this object is defined by the next few statements. Like,

[line 31] - model.name('thermo_refractive_COMSOL_1D_axisymmetric_model.mph');

> The 'model.param' contains all functions related to setting and describing the parameters in the model.

*Note that the 'param' following keyword 'model' connected by the '.' has nothing to do with the 'param' structure used in the script "Main_thermo_refracive.m" which have been named anything else

> Now the model.param.set(<P>,<expr>) is used to give the parameter P an expression expr both being string.

The model.param.descr(<P>,<des>) has the same format but gives the description of the parameter P as des (something that is understandable in common terms).

This can be understood in the statements in [line 46 - 51]

An empty quote in the description implies that no description is given. The above statements define the parameters mentioned alongside them according to Heinerts paper.

> [line 53-61]. the string 'var1' is used to tag all the global variables that are created. variables are expressions created out of the parameters.

Just like the above case, 'set()' is used to create variables and give them an expression, here as one can see 4 variables are created T_amb, beam_size, beam_power. and f_mod.

> The next section deals with the geometry. In this case the model is a 1D axisymmetric model. Hence one has the the digit 1 which specifies the dimension and axisymmetric is set to 'true'

model.geom.create('geom1', 1);
model.geom('geom1').axisymmetric(true);

> The run() function is to build the geometry

model.geom('geom1').run;

> The 'Interval' feature is present in the case of 1D models. The following line creates an interval feature called 'i1'

model.geom('geom1').feature.create('i1', 'Interval');

model.geom('geom1').feature('i1').set('p2', num2str(param.mirror.radius));

The above line is used to set the value of the right end-point as the radius of the mirror. The string 'p2' is used to denote the right end point..

So this step creates a cylinder of radius equal to the radius of the mirror. In case of an infinite mirror an extra interval is added from the the radius to twice the radius.

It would help if more description on "interval" is left as comments and on why the extra interval was added and how does it make the calculation different.

> The interval is run using the 'run()' command.

The following lines cannot be understood. Comsol help on"propertyGroup" gives no results found

> The meshing is done on auto.

> As far as the Physics is concerned i.e. what kind of results we expect out of this geometry, the 'HeatTransfer' is selected.

A 1D heat source is created called 'hs1'

model.physics('ht').feature.create('hs1', 'HeatSource', 1);

and the Heat Source is time varying and given by beam_intensity*sin(2*fmod*pi*t). This can be seen in lines 121-122

model.physics('ht').feature('hs1').selection.set([1]);
model.physics('ht').feature('hs1').set('Q', 1, 'beam_intensity*sin(2*fmod*pi*t)');

> If the mirror is infinite, something called 'InfiniteElements' is applied to the outer interval. More details on "infiniteElements" and why was it used would be helpful.

> A study involving the feature "Transient" was used. However, it is required to know what study was implemented from the GUI since the term "Transient" was not found under Study Steps in the GUI

model.study('std1').feature.create('time', 'Transient'); [line 134]

> The time step tweaking of COMSOL is stopped by the following line 166

model.sol('sol1').feature('t1').set('tstepsbdf', 'strict');

**The point where the feature called 'Transient' is spoken about - By selecting 'Time Dependent' under the 'Study' in COMSOL desktop, the line that gets added to the Matlab script.

So it was the 'Time Dependent' feature that was selected while creating the model

Tue Jun 11 17:04:33 2013

Analyzing the file 'thermo_refractive_COMSOL_1D_axisymmetric' by Koji Arai

The file 'thermo_refractive_COMSOL_1D_axisymmetric.m' found in the SVN repository https://nodus.ligo.caltech.edu:30889/svn/trunk/comsol/thermo-refractive/ performs the data extraction from the COMSOL simulation

and computes quantities as given in Heinert's paper.

This is the where the dissipation is calculated from the temperature gradient and the use of FDT is made to evaluate the linearized PSD.

The first few lines of the code extracts the variable values out of the structure 'param' and stores it in new variables for the ease of coding.

The important portion comes in with the iterative structure (for loop) in line 29.

A point wise summary of the steps done would be as follows -

* The finite elements in space and time are defined in the arrays r0 and t0 according to the time and radial slice steps dt and dR until R, the radius and the t_end, the time until which simulation runs

* A matrix called dat is created which is used to store the values of the temperature gradient as returned by COMSOL.

It stores the values as a function of r along the columns and as a function of t along the rows.

Thus, moving vertically down the matrix in a column would give the values of the temperature gradient for a fixed r as a function of t

* Two other row vectors datrabs and datrphs having lengths of the array r0 are used to store the values of the square of the Fourier coefficients and the phase angle.

* The extraction of data from COMSOL is done in the lines 71-74

    for i2=1:length(t0)
       tmp = mphinterp(model,'ht.gradTr','coord',r0,'T',t0(i2));
       dat(:,i2) = tmp;
    end

* After the above step, the matrix dat is filled with the values of the temperature gradient as mentioned previously.

* Next to evaluate to the Fourier coefficients, the second half of the simulation time is used. Probably to let the transients die down as mentioned in the ELOG post by the author.

* To find out the Fourier components, we multiply the desired function by sin(omega*t) or cos(omega*t) and integrate over the period of the function. There is also a prefactor of 1/L where L is the length of the period

over which the function is defined.

* To do the above exercise, the sine and cosine of omega*t is separately evaluated and stored in skernel and ckernel. Note that the time interval as mentioned above is the second half of the simulation time.

* Now for all the radial slices, the Fourier coefficients are extracted using the statements in for loop in line 83

    for i2=1:length(r0)
       tseries=detrend(dat(i2,(length(t0)+1)/2:length(t0)));
       tmp1=mean(tseries.*skernel);
       tmp2=mean(tseries.*ckernel);

       datrabs(i2)=2*sqrt(tmp1^2+tmp2^2);
       datrphs(i2)=atan2(tmp2,tmp1)/pi*180;
    end

Using the definition of mean of a function ' f ' in the continuous case as f_mean = integral{ f(t)dt} / integral{ dt } , over the values of t

tmp1 has used ' f ' as tseries.*skernel which means that one multiplies the time signal with sin(omega*t) and integrates. tmp2 has used cosine instead

Thus, tmp1 and tmp2 are the Fourier coefficients of tseries at the frequency fmod defined right close to the first for loop in line 29.

* The coefficients are squared and added in the line 88

datrabs(i2)=2*sqrt(tmp1^2+tmp2^2);

This quantity how much of the frequency ' fmod' is present in the time signal.

datrphs stores the same for the phase shift phi. Note however, all of this is done as a function of r. The plotting is done in the following lines. Note that while running the code, as a result, the plots are seen to
get updated each time the loop [line 29] iterates.

* Following this, is the part where W_diss, the dissipation is calculated using formula [The expression used does not match Eq. 15 in Heinert's. Any comments regarding the formula used for W_diss are welcome].

The heinert's eq(15) goes as - W_diss = pi*H*kappa/T0 * integral{ grad_T^2 * rdr }

The quantity datrabs is squared and the integral mentioned above is calculated w.r.t. r using the trapz algorithm from Matlab.

The value for each frequency i.e. each 'fmod' is converted to a string and displayed on screen.

* The reason why the grad_T was changed to its frequency domain before integration is suspected to be something related to the Parseval's Theorem. However, more details or correction on the same is welcome.

Mon Jun 17 11:06:17 2013

Plans for the week of 6-17-13 through 6-22-13

This week I will update my previous eLog entry with a nicely labeled plot showing both lines on the same plot, then I intend to implement improved meshing on the mirror in the COMSOL model I have constructed, increasing the number of elements on the mirror's face and the central axis of the mirror such that there are more elements in the regions where the applied force is greatest. This should result in more accurate and faster to compute simulations, allowing us to increase the number of elements in the mesh and possibly reduce the residual and allow us to use the better gravitationally balanced boundary condition and obtain an answer which converges. Afterwords, I intend to look at sample code showing how to use Matlab in conjunction with COMSOL since we will need to do so for my project. If there is time remaining later in the week, I will attempt to replicate some of the results Steve Penn generated in order to verify my model.

Wed Jun 19 14:59:13 2013

The Relative Residual Convergence Error

We have been encountering an error in COMSOL for a while of the form "Failed to find a solution.; The relative residual (###) is greater than the relative tolerance.; Returned solution is not converged.; -Feature: Stationary Solver 1 (sol1/s1); -Error: Failed to find a solution." The error has occurred when attempting to find a stationary solution in models with boundary loads and no fixed constraints (preventing an edge from moving). We wanted to determine what the error was caused by to allow us to use the stationary solver, or at least to confirm that the error was not indicative of a problem in our model. To this end, I designed a few very simple COMSOL models in which I was able to reproduce the behaviour and attempted to determine the root of the issue.

I first constructed a somewhat similar model to ours using a cylinder of fused silica with all of the default values and a normal meshing. I applied a boundary load of 1N on one of the faces and ran a stationary solver. As expected, the solver failed to converge since it had no boundary condition preventing it from accelerating continuously. Applying a force of 1N on the opposing face resulted in the same error as above, which replicates the previous error since the system is failing to converge in a case where it should. I decided also to make an even simpler 2-D model of a square. Applying 1N forces to opposing sides on the square again returned the error above.

Both of these models were able to be evaluated using at least an eigenfrequency solver as noted on the primary model in the previous eLog. I looked on the COMSOL forums and read through some more of their documentation and saw the suggestion in response to this error to use a time-dependent solver and simply view times after the system will have settled to a stationary state (#2 https://community.cmc.ca/docs/DOC-1453). I attempted this on the test models and both of the time dependent solutions converged without error to their expected solutions (compression between the faces on which forces were being applied). This may be a sub-optimal computational method though as even in the simple cylinder case with 6133 elements and a simple force profile, the solution took several minutes to run. For the cylindrical model, I evaluated the strain energy using both an eigenfrequency and time dependent solver and obtained the same result using both of the solvers. The eigenfrequency solver evaluates much more quickly than the time dependent solver, and in the primary model as I noted in my previous eLog, the strain energy obtained using the eigenfrequency and frequency domain solvers agreed, so it seems that the best manner in which to proceed is to use the eigenfrequency solver to compute the strain energy.

The source of the error is still unknown, but given these tests, it seems very unlikely to be indicative of a problem in our model. We still have a very significant disagreement between the simulated results and the calculated values. I am going to spend the next day or so looking through both the COMSOL model and the analytic calculation and checking them for errors which could cause this discrepancy. I will then start reading the documentation on Livelink for Matlab and try to implement it.

Thu Jun 20 10:26:38 2013

Matt A.

The Relative Residual Convergence Error

Emory:

I don't understand how you're getting the strain energy from the eigenvalue solver. It is my understanding that the eigenvalue solver will only give you the strain energy at a particular eigenfrequency. We're interested in the strain energy from the beam deformation at frequencies below the first eigenmode.

Quote:

Thu Jun 20 12:41:01 2013

The expression for the "work dissipated" in the TE and TR noise calculations

While discussing TE noise with Yanbei Chen, it was realized that the expression for the work dissipated W_diss was derivable from the inhomogenous Heat equation with a source term.
The exercise was tried out to some success and can be found in the attachment. The attachment describes the steps roughly.
The important point to note is the fact that while Liu and Thorne considered stresses developed in the material by means of the heat balance equation, they have ultimately resorted to the
expression for W_diss = 1/T * integral{ kappa * grad(T)^2 rdr } to calculate the dissipation. They have used an expression whch relates the expansion, Theta, to the gradient of temperature.

It is suspected that the fundamental approach is to consider a source of heat and evaluating the dissipation. However, Liu and Thorne considered applying pressure probably because of the
physical scenario of the fluctuations in the mirror face.

Discussion over the same would be helpful.

Attachment 1: dissipated_work.pdf

Thu Jun 20 12:51:44 2013

The Relative Residual Convergence Error

I used the same integrator that we had setup for use with the stationary solver. I had expected it to either fail or return a very different result, but assumed that the fact that it was returning the same result as when it was used after the previous solvers indicated that it was able to use that solver to find the value. After seeing this comment I went back and checked and the solver was setup to use the last stationary solution regardless which solver last ran. I will run the previous tests which relied on using this integrator in conjunction with non-stationary solvers again and see if they actually agree and how the results they give compare to the analytic solution. I will spend some time today trying this. Unfortunately, both the time dependent and frequency domain solvers take a long time to converge, so running these tests may take most of the day, but I can start reading through some of the Livelink for Matlab documentation while they run.

edit:

I ran the time-dependent solver for the rigid back boundary condition and computed the strain energy for the final two time-steps. Both of them gave a value of 1.58425*10^-10 J which corresponds to Sx(100 Hz)=2.08871*10^-40 which is about 3.6% greater than the value obtained from the stationary solver. I don't understand why these values would differ at all. When I tried to run the time dependent solver with the spring back and gravitationally opposing force boundary conditions an error message was returned: "Failed to find consistent initial values., Last step is not converged.; -Feature: Time-Dependent Solver 1 (sol4/t1).; -Error: Failed to find consistent initial values."

I'm going to spend some more time looking at the COMSOL model attempting to find anything which could be causing this error and reading any relevant documentation I can find.

edit 2:

I spent most of the day attempting to find the source of either of these errors. Possible solutions I found and tried included increasing or decreasing how fine the mesh is, increasing the acceptable tolerances, and increasing the time interval in the time dependent solver. I attempted all of these and none of them worked. Surprisingly, when I increased the acceptable tolerance level for the stationary solver, it returned a greater relative residual which does not make sense to me.

I also took the simple 3d cylinder constructed yesterday and was able to replicate the errors with it. When I increased the time interval on that case for the time dependent solver, it converged and gave a result. I was able to get a Umax value for the final time step, which should be equivalent to the one which we would expect a stationary solver to return. Further increasing the number of time steps the primary model computed did not cause it to converge. I will run this again with many more time steps and see if it converges. Even if it does, this doesn't seem like a good way to do our computations as it takes a long time to complete a solution, but seeing whether it converges may give us information on what the problem with the stationary solution is, in particular if increasing the number of time steps does cause it to converge, then that would indicate that finding a way to make the simple case converge would probably work for our model as well.

Quote:

Emory:

Quote:

Sun Jun 23 14:00:05 2013

Manipulating the Relative Tolerance

We have been seeing an error when attempting to use a stationary solver in conjunction with a set of boundary conditions which does not fix the face of the mirror opposite the applied force. I have tried a number of settings changes and tweaks in order to attempt to get the stationary solver to converge on our model. I have found that by switching to the PARDISO solver and increasing the relative tolerance to 500, the solution will converge (Umax=1.49866*10^-10 J). This does require increasing the relative tolerance greatly, which is concerning. After doing this, I also found that by increasing the relative tolerance to 700 and using the SPOOLES solver it also converged giving Umax=1.498653*10^-10 J. The fact that these agree quite well indicates that the increase in relative tolerance may not have harmed our values. If this were a more complicated system which we would expect to have behaviour which could cause our solvers to get stuck on a set of values I would be more concerned, but I think that this may be a workable fix in this case. These values of Umax give Sx(100 Hz)=1.97586*10^-40 m^2/Hz which differs by about 5% from our previous value of Sx(100 Hz)=2.08291*10^-40 m^2/Hz. Unfortunately, this seems to indicate that the difference in results between the COMSOL model and our direct computation is not due to a difference in boundary conditions. I will spend some time looking for more useful documentation on the relative residual, relative tolerance, and LU factorization: out of memory (despite having more RAM availiable) error, then I will work through our COMSOL model again, possibly remaking it, and check it for any errors which could result in the disparity between our simulated and directly computed results.

After doing this, I was able to find more information on the relative tolerance in the COMSOL release.book (page ~30 https://www.tuegrid-doc.uni-tuebingen.de/dokuwiki/lib/exe/fetch.php?id=hpc-uni%3Asoftware-docs%3Acomsol%3Acomsol&cache=cache&media=hpc-uni:software-docs:comsol:release.pdf). It appears that the relative tolerance and the Factor in error estimate values jointly determine the maximum allowed difference between successive estimates when using an iterative solver. I decided to try to get a better idea for this behaviour, so I increased the Relative tolerance to 10000 and surprisingly obtained the same result as before. I think I am going to recreate our COMSOL model without any unnessesary things implemented and only include a stationary solver, then run this test again as it seems like this should have had some affect on the output.

Fri Jun 28 14:03:07 2013

Approach for TE noise for beam in cavity

In this post I mention of the approach that would be taken to solve for the TE noise spectrum for a beam inside the substrate cavity.

Completing the same would be my plan for the next week.

In the COMSOL simulation, a gaussian pressure will be applied on both the flat surface of the cylinder. The strain would be calculated
using the Structural mechanics module and the temperature field would be calculated using the Heat Transfer module. The approach
is similar to that followed in Liu and Thorne. The Work dissipated would be calculated using the gradient of T. The spectral density is
then calculated using the FDT.

In the attachment, I have written briefly about the material I have studied this week along with my thoughts on the problem of the TE noise
calculation.

Attachment 1: LL_derivations.pdf

Wed Jul 10 17:52:18 2013

Koji

How to force time steps for a time dependent simulation

A common trap in COMSOL:

When you run a time series simulation, COMSOL tries to be "clever" by skipping some time steps
and returns you an interpolated result in order to accelerate the calculation.
But for certain types of applications, such as time series response analysis by applying periodic force/heat,
this "clever" adaptive algorithm messes up our calculation.

You can apply forced time steps by giving a specific option:
- In Model Builder, open your study. Then open your Solver
- Click "Time-Dependent Solver" in Model Builder
- You get bunch of options in Time-Dependent Solver pane.
Open "Time Stepping".
- Change "Method" from "Generalized alpha" to "BDF".
- Change "Steps taken by solver" to "Strict"

Then, you should be OK.

This can be done by

model.sol('sol1').feature('t1').set('tstepsbdf', 'strict');

in COMSOL with MATLAB. (Of course sol1 and t1 should be changed appropriately.)

Thu Jul 11 19:16:12 2013

The present aim is the calculation of the TE noise like Liu and Thorne. Although, the results of Liu and Thorne are for the case of an infinite mirror, in our case, we try
to model a test mass with large dimensions in an attempt to get closer to the result due to Liu and Thorne

Following my previous post - The presents results given by the COMSOL simulations gave the same profile as Liu and Thorne's result which has a frequency dependence
of 1/omega^2 but was displaced from the analytic result by a constant factor which was dependent on the applied pressure on the face of the test mass which should not be
the case.

Following the steps followed Liu and Thorne, we had constructed the test mass as a cylinder, large compared to the beam spot size. An oscillating pressure was applied
to one of the faces and the from the temperature gradient generated in the process due to strains, one can calculate the work dissipated. The process involves integrating
the gradient of temperature over the entire geometry and taking the time avrage. However, this did not give the correct results, so it was decide to extract the Fourier coefficient
of the signal and perform the integration on it, as done in the case of TR niose by Koji Arai.

I mention the steps it was done -

> The data extracted was stored in a 3D array in matlab. using mphinterp - each dimension for r, z, t

> The number of radial slices and z slices is defined by the user previously

> For each r,z value there was a time signal.

> The fourier coefficient corresponding to the pressure oscillation frequency was extracted from the last three cycles
(In theory only one cycle should suffice)

> The above step was done so that random data( which is small in magnitude) generated by COMSOL is avoided.

> The fourier coefficients are stored in a 2D array corresponding to r and z values.

> The integration was performed using trapz twice once on each dimension to get the total volume integral

> The rest of the calculation is same as the previous script - plugging in the prefactors in the formulae and plotting

**The primary problem with this script is that the data extraction takes significant amount of time - For a mirror with 200 times the radius of the beam spot and 200 radial slices, it takes close to 6 minutes
to evaluate work dissipated for each frequency. The script solves for 16 frequency values. The results for small number of radial slices does not follow the straight line profile. For larger number of slices
the program takes a longer time. The results have not been checked yet.

Attachment 1: TE_model.m

% TE calculation using 2D axisymmetric model. This script calls the model
% file, extracts grad_T and does the calculations for the different
% frequency
% All parameter are defined in this script and passed to the COMSOL model
% via arguments
% Parameters, Quantitites in [m]
param.beam.radius = 0.05;
param.mirror.radius = 100 * param.beam.radius; 
%Define the radius of the mirror as 100 times that of the beam radius
param.mirror.height = 200 * param.beam.radius;

... 94 more lines ...

Attachment 2: almost_infinite_2D_axisym_TE_4.m

function out = almost_infinite_2D_axisym_TE_4(param)
% Putting all the parameters in the variables
r0 = param.beam.radius;
R = param.mirror.radius;
H = param.mirror.height;
dt = param.COMSOL.simulation_time_step;
fmod = param.COMSOL.fmod;
t_end = param.COMSOL.simulation_end_time;
p0 = param.constant.F0/(pi*r0^2);% The amplitude of Osc. pressure
T_amb = param.constant.T_amb;

... 121 more lines ...

Fri Jul 12 19:43:32 2013

Quote:

I mention the steps it was done -

> The data extracted was stored in a 3D array in matlab. using mphinterp - each dimension for r, z, t

> The number of radial slices and z slices is defined by the user previously

> For each r,z value there was a time signal.

> The fourier coefficient corresponding to the pressure oscillation frequency was extracted from the last three cycles
(In theory only one cycle should suffice)

> The above step was done so that random data( which is small in magnitude) generated by COMSOL is avoided.

> The fourier coefficients are stored in a 2D array corresponding to r and z values.

> The integration was performed using trapz twice once on each dimension to get the total volume integral

> The rest of the calculation is same as the previous script - plugging in the prefactors in the formulae and plotting

I am replying to report of the modification made to the script from the last one. The problem of too many radial and z slices have been avoided by using a slicing based on a gaussian
distribution both along the r and z directions - i.e. the slicing is heavy in the region around the surface is applied and much thinner towards the edges of the cylinder. The slicing has
been separately handled by a function named giveSlices() which does the slicing and returns the values as two arrays corresponding to r and z.
The extent to which the fineness of slicing is controlled in the geometry is by controlling the parameter SD in the code which is the standard deviation of the gaussian according to which
the slicing is controlled as being fine throughout or fine in the centre and thin with increasing r.

This method reduces the number of slices by almost 2 orders for significant large values of the dimensions of the test mass while it is expected to give similar results since slicing the
test mass finely at the edge is not required as the gradient of temperature almost falls to zero.

It is suspected that the long time of simulation is attributed to calling mphinterp() command a large number of times. In my next modification, it will be tried to use the command just once
followed by the proper data extraction from the output given by the command.

Attachment 1: codes_TE_calc.zip

Sun Jul 14 15:13:46 2013

Quote:

I mention the steps it was done -

> The data extracted was stored in a 3D array in matlab. using mphinterp - each dimension for r, z, t

> The number of radial slices and z slices is defined by the user previously

> For each r,z value there was a time signal.

> The fourier coefficient corresponding to the pressure oscillation frequency was extracted from the last three cycles
(In theory only one cycle should suffice)

> The above step was done so that random data( which is small in magnitude) generated by COMSOL is avoided.

> The fourier coefficients are stored in a 2D array corresponding to r and z values.

> The integration was performed using trapz twice once on each dimension to get the total volume integral

> The rest of the calculation is same as the previous script - plugging in the prefactors in the formulae and plotting

Following the previous reply regarding the use of mphinterp(), the appropriate changes in code were made. The overhead time due to the call to COMSOL was responsible for the longer
simulation time. Right now, for relatively large no. of total slices (about 27000) just the extraction of data happens within a few seconds. However, for the larger number of slices, the codes
will probably still take some time to complete. The codes are attached.

Attachment 1: codes_TE_calc_(2).zip

Mon Jul 15 16:05:29 2013

Quote:

I mention the steps it was done -

> The data extracted was stored in a 3D array in matlab. using mphinterp - each dimension for r, z, t

> The number of radial slices and z slices is defined by the user previously

> For each r,z value there was a time signal.

> The fourier coefficient corresponding to the pressure oscillation frequency was extracted from the last three cycles
(In theory only one cycle should suffice)

> The above step was done so that random data( which is small in magnitude) generated by COMSOL is avoided.

> The fourier coefficients are stored in a 2D array corresponding to r and z values.

> The integration was performed using trapz twice once on each dimension to get the total volume integral

> The rest of the calculation is same as the previous script - plugging in the prefactors in the formulae and plotting

The dependence of the Power Spectral Density on the parameters F0, which is the pressure amplitude, has been somewhat corrected for in the codes attached. The mistake lay in the fact that
extraction of the Fourier coefficients was being done for the ht.gradTmag, the Fourier coefficients of which are not the correct ones to be used in this case since ht.gradTmag is not the correct time signal.
In the present case the Fourier coefficients are extracted from the r and z components, squared and added to carry out the calculation. However, the results are still off from the L&T results by order of 5.
The codes and the plots are attached.

The red values are the L&T result while the blue sketch is the simulation

Attachment 1: codes_TE_calc.zip

Mon Sep 16 10:07:32 2013

Evan

COMSOL 4.3 on the OS X command line

If you're running Matlab scripts that iterate over simulation parameters (à la Tara), you might find it useful to be able to run everything from the command line (instead of launching the "Comsol with Matlab" GUI application).

First, the comsol command wasn't in my path, so I symlinked it to someplace where bash could find it:

ln -s /Applications/COMSOL43a/bin/comsol /opt/local/bin/comsol

I then started Comsol/Matlab using a slight modification of the commands given in the Comsol 4.3 help file "Running A COMSOL M-file In Batch Mode Without Display":

comsol server > server_log.txt &

matlab -nodesktop -nosplash -r "run /Applications/COMSOL43a/mli/mphstart; comsol_script; exit"

The first command starts the Comsol server in the background and cats its output into a log file. The second command launches Matlab, runs the initialization script which makes Matlab aware of Comsol, runs my Comsol/Matlab script (comsol_script.m), and then exits.

Thu Apr 17 16:52:09 2014

Evan

Interpreting logfiles and picking a solver

Characterization

Here are two entries by Walter Frei on the Comsol blog that I've found useful.

Solving Linear Static Finite Element Models: Tells you how to interpret all those numbers that Comsol dumps into its logfiles.

Solutions to Linear Systems of Equations: Direct and Iterative Solvers: Explains a bit more about Comsol's solvers. Apparently, PARDISO is usually fast and SPOOLES is usually slow (the tradeoff is apparently that SPOOLES uses less memory). I've found this to be personally true with at least one model I've worked with.

Tue Sep 30 11:30:27 2014

Here is a set of slides by Yoichi Aso on how to handle gravity in Comsol.

101

Sat Sep 5 15:17:41 2015

I moved the only entry from the 'ENG_FEA' log into the COMSOL log and then renamed that logbook as 'FEA' since we don't need two FEA logs.

Also renamed 'AdhikariLab' log as ATF.

102

Fri Dec 4 18:32:02 2015

COMSOL: remote server w/ matlab

This summarizes how to get the remote comsol server to run. COMSOL 5.1.0.234 is now on tegmeni thanks to Larry.

On the server:

rana@tegmeni|~> /usr/local/comsol51/multiphysics/bin/comsol server -login force

This starts up a comsol server instance, listening on port 2036. '-login force' will ask you to supply a username and password which you make up. You will have to enter these later from the client side.

On my laptop, from the MATLAB prompt:

>> addpath('/Applications/COMSOL51/Multiphysics/mli/')

>> mphstart('tegmeni.ligo.caltech.edu', 2036,'uname','pword')

That's it! Now you just run the matlab script which runs the COMSOL file.

I'm attaching a tarball of the .mph file (written by Dmitry Kopstov from MSU) and the associated matlab scripts which change the parameters, as well as looping over test mass thickness to produce a plot of Brownian noise PSD v.

Attachment 1: BrownianSweep.tgz

109

Sun May 7 18:22:35 2017

Voyager ITM: Radiative cooling with cold shield and cold CP

Voyager

I took Aidan's COMSOL model for the ITM from a couple years ago and updated it with some more details:

Through radiative cooling only, the ITM is cooled to 103 K. Taking it to 123 K will be accomplished by adding a ring heater to the ITM.
Assume 3 W of heating from main laser beam onto ITM HR face.
Emissivity of ITM barrel is 0.95. Emissivity of HR* and AR faces is 0.5.
The CP and the Inner Shield are kept fixed at 80 K. This is to simulated the effect of having conductive cooling with cold straps. This needs to be checked in more detail by actually modeling thermal straps.
Emissivity of the CP is 0.9.
The total length of the inner shield is 5 m. The CP is at z = 0 m and the ITM is at z = 2.25 m. We should check what the result would be if the shield is ~1m shorter or longer.

In the attached image, I have made one quadrant of the tubular cryo shield transparent just for clarity - the actual modelled tube is 3 cm thick, made of aluminum, has an emissivity of 0.95 on the inside and 0.03 on the outside (to simulate what we would get from polished aluminum or gold coating).

This files is in our GitLab: https://git.ligo.org/rana-adhikari/CryogenicLIGO/blob/master/FEA/ITM-ColdShield-CP.mph

*I am suspicious of just using a single emissivity number for the AR and HR coatings. Since we are concerned with wavelengths which are long w.r.t. the coating thickness, it may be that the HR and AR coatings have a complicated wavelength dependence in the 5-50 micron band.

Attachment 1: ITM-ColdShield-CP.png

110

Mon Jul 24 15:35:34 2017

Mariia

Running Comsol to Matlab

WIth Gautam's help, I have created a user directory in 40 meter Lab and copied Rana's documents (MATLAB coating files) from flash card into it. After that, from this elog by Rana : COMSOL: remote server w/ matlab from Fri Dec 4 18:32:02 2015, ran the matlab document BarrelCoating which resulted in the following error

Messages:

Could not obtain license for#LiveLink for MATLAB

Could not obtain license for LiveLink for MATLAB.

License error: -4.

Licensed number of users already reached.

Has anybody seen this before?

111

Mon Jul 24 15:54:26 2017

Koji

Running Comsol to Matlab

The number of licenses already used by whom / still remains can be confirmed by running the following command on a comsol-installed linux machine

$ cd /usr/local/comsol51/multiphysics/license/glnxa64 $ ./lmstat -c ../license.dat -a

112

Wed Jul 26 20:14:46 2017

Running Comsol to Matlab

I've just tried this out on my desktop machine using COMSOL 5.1 and its still working. Which COMSOL is installed on optimus at the 40m ?

113

Fri Jul 28 15:48:58 2017

Mariia

Comsol batch for windows

Using the written path from elog by ericq: Computer Scripts/Programs, Comsol can be run from the directory on the distant computer: /cvs/cds/caltech/apps/linux64/comsol51/bin/glnxa64/comsol batch -inputfile Model1.mph -outputfile Model_solv.mph. To transfer files from Linux to Windows : the command pscp.

The method:

1. To download PuTTY and make a coonection with a distant computer.

2. Linux terminal: ssh optimus % allows to go into the whole system

3. Windows terminal: pscp "the path of the file" controls@nodus.ligo.caltech.edu:/users/.../ % allows to transfer mph-file from Windows to Linux

4. Linux terminal: /cvs/cds/caltech/apps/linux64/comsol51/bin/glnxa64/comsol batch -inputfile Model1.mph -outputfile Model_solv.mph % calculation on the distant computer, without outputfile solution would be stored in the input file

5. Windows terminal: pscp controls@nodus.ligo.caltech.edu:/users/.../Model_solv.mph Documents\ % copy file from Linux to Windows, Documents is the name of the folder in Windows

114

Mon Jul 31 22:18:57 2017

using more than 12 cores in matlab

Since 2014, the limit of 12 workers using the matlab parallel computing toolbox has been lifted. Today, I was able to get this to work. There's a trick.

Usually, when you start up matlab and run a parallel thing like 'parfor', it just uses a default profile 'local' which limits you to 12 workers. You can try to ask for more by doing 'parpool(40)' for 40 workers, but it will tell you that NumWorkers = 12 and you're out of luck. So instead:

myCluster = parcluster('local')

myCluster.NumWorkers = 40;

saveProfile(myCluster);

parpool('myCluster', 40)

It seems that it needs the max # of workers and the requested number of workers to be 40 to use 40, otherwise you'll just get 12 (as of matlab 2016a).

Attachment 1: Screen_Shot_2017-07-31_at_10.11.35_PM.png

127

Sat Mar 17 15:27:48 2018

file size >> small

When saving your COMSOL files do these two things to make the files much smaller (good for saving in version control and sharing):

File -> Compact History
Preferences -> Files -> Optimize for File Size (not speed)

128

Mon Aug 20 15:44:56 2018

file size >> small

Also,

click 'Clear Mesh' under the mesh menu
'Clear Solutions' under the Study menu

In this way the file sizes will be ~100 kB instead of 10's of MB.

Quote:

When saving your COMSOL files do these two things to make the files much smaller (good for saving in version control and sharing):

File -> Compact History
Preferences -> Files -> Optimize for File Size (not speed)

130

Sun Aug 26 19:21:27 2018

Voyager ITM: Radiative cooling with cold shield and cold CP

Voyager

this is a time dependent model of the previous steady-state one

Cold Shield and CP held at a constant 60 K
3 W heat input to the ITM from the main laser beam
radiative cooling to the shield
ITM barrel emissivity = 0.9
ITM HR/AR emissivity = 0.5/0.5

So the cooldown time w/o a heat switch is ~4 days. Since this is less than the usual pumpdown time required to open the gate valves on the beamtubes, perhaps no heatswitch or in-vac cryogens are required.

Attachment 1: ITM-Cooldown.pdf

Attachment 2: CoolDown.webm

138

Tue May 12 14:16:28 2020

Koji

FEA tutorial resources

cf. Forwarded email from Stephen

1) Tuesday Demo - Basics of FEA Meshing G2000696
2) CIT SYS User Guides, How to Use the FEA User Group T2000295
3) CIT SYS User Guides, How to Use the ANSYS Learning Hub T2000236

Fabrice's SAMS piezo actuator second prototype E1900383

139

Tue Aug 11 11:16:29 2020

aaron

COMSOL with Matlab without display

When running comsol with matlab interface on sandbox1, it is usually most convenient to ssh with screen forwarding (eg '-CY') and launch COMSOL with matlab by following the instructions in the livelink manual.

Sometimes, it is necessary to run COMSOL without any display available. In that case, the Instructions in the manual are a little unclear. Here are the detailed steps that let me run my script '/home/amarkowi/metamaterials/run_spiral.m' with no screen forwarding.

1. ssh onto sandbox1 by entering the following at your laptop command prompt

Aaron’s-latpop $ ssh aaron.markowitz@sandbox1.ligo.caltech.edu

password: [enter sandbox1 credentials]

2. start a tmux session for starting the COMSOL server

aaron.markowitz@sandbox1:~$ tmux

3. start a comsol server from the tmux session

aaron.markowitz@sandbox1:~$ comsol54 mphserver -login force -port 2020

Username: whoever

Password: whatever

Confirm password: whatever

4. detach the tmux session by pressing ‘ctrl-b’ followed by ‘d’

5. (optionally, you can start a new tmux session for your matlab work by running tmux again at your main sandbox prompt)

6. Start matlab by running

>> matlab -nodesktop -mlnosplash

6. Add the comsol directory to the matlab path by running at the matlab prompt

>> addpath(‘/localhome/comsol54/multiphysics/mli/‘)

6. Start the matlab with comsol interface by running the following at the matlab prompt

>> mphstart(’sandbox1.ligo.caltech.edu’, 2020, ‘whoever’, ‘whatever’)

7. change into the directory containing the script, and run it

>> cd /home/amarkowi/metamaterials

>> run_spiral

140

Tue Aug 11 16:35:07 2020

aaron

COMSOL: remote server w/ matlab

To run COMSOL on sandbox1 with no graphical Interface, here are the steps that worked for me (Tue Aug 11 16:35:51 2020) from a mac on the Caltech VPN.

1. ssh onto sandbox1 with screen forwarding (-Y). Make sure you have a compatible version of XQuartz or a substitute. -C specifies data compression, which may be useful on slow connections

Aaron’s-laptop $ ssh -CY aaron.markowitz@sandbox1.ligo.caltech.edu

password: [enter sandbox1 credentials]

2. Launch Matlab with COMSOL 5.4, specifying no graphical interface, by running

aaron.markowitz comsol54 mphserver matlab -nodesktop -mlnosplash script_name’

3. If there is still a splash screen from the COMSOL server, you will have to specify nosplash by adding the following line to your .bash_profile (in your home directory)

export COMSOL_MATLAB_INIT=’matlab -nosplash’

4. You can run whatever comsol script you need. Make sure that in your script you import the comsol functions by calling the following

import com.comsol.model.*
import com.comsol.model.util.*

141

Thu Jun 22 14:12:04 2023

Raj

Finesse Modelling for aLIGO

aLIGO

The aLIGO model available on IFOSim uses the first surface of the mirror as Port 1 and the other surface as Port 2. This requires us to use negative radii of curvatures among others to get the correct modeling. However, this makes adding surface maps more difficult and was causing issues with getting the simulations to follow what is expected. The surface_map attribute for mirrors doesn't allow us to specify the mirror port in Finesse.

Following a discussion with Kevin, it seems that this approach is being deprecated. His suggestion is to use node 1 as the front of a mirror and node 2 as the back of the mirror. And likewise nodes 1 and 2 as the front of a beamsplitter and nodes 3 and 4 as the back.

I am rewriting the IFOSim aLIGO model with this convention to allow for later simulations not to be plagued by issues and allow for easier simulations of the beam.

142

Thu Jul 6 11:35:55 2023

Rajashik

Basic Demonstration of Cavity Scan

Attached are plots of how HOMs are introduced by defects in the mirror. This is just an example for a basic FP Cavity.

Attachment 1: before-min.png

Attachment 2: after-min.png

100

Sat Sep 5 15:04:43 2015

Dennis Coyne

summary of FEA modal model to State Space model

At the 2014 commissioning workshop, I presented a summary of my efforts in converting finite element modal models into state space models:

https://dcc.ligo.org/LIGO-G1400099

I also provided the attached written summary for a report on the workshop that Aidan Brooks and Gabriele Vajente are preparing.

Attachment 1: FEM2SS_summary.docx

105

Tue Jun 28 15:50:45 2016

Joy Westland

A Simple Model of the Modal Analysis of a Cantilever Circular/Cylinder Cross Section in ANSYS tutorial

Analysis

Here is a tutorial to implement a simple Modal Analysis of a Cantilever Cylinder

1. Open the ANSYS workbench

2. Drop and drag the "Modal" analysis system into the project schematic

3. Right click on "Engineering Data" and edit the material. There are predetermined properties found in the "Engineering Data Sources" (Right click on the description or press the books in the top right hand corner). For this tutorial, fused silica was created with these parameters:

Young's Modulus E: 7.2E10 Nm^-2 (Isotropic Elasticity)
Density p: 2200 kgm^-3 (Density)
Specific Heat c: 770 J/kgK (Specific Heat)
Isotropic Thermal Conductivity k: 1.38 W/mk (Isotropic Thermal Conductivity)
Coefficient of Thermal Expansion: 3.9E-7 (Isotropic Secant Coefficient of Thermal Expansion)
Reference Temperature: 21 C (Isotropic Secant Coefficient of Thermal Expansion)
Poisson's Ratio: 0.17 (Isotropic Elasticity)

In order to put in the parameters, just drag and drop from the toolbox. Also make sure the filter is turned off (that's the filter symbol next to the engineering data sources/books in the top right hand corner) this will allow a user to few all the parameters.

4. Return to the project, and open/edit the geometry. The cantilever that was used for this tutorial is a cylinder with a diameter of 2 mm with a length of 200 mm, shown in image 1.

How to Create a geometry:
- Open up the geometry
- Decide which plane you want to start drawing in: XY Plane, ZX Plane, YZ Plane
- Click on "new sketch" in the 4th row from the top after "Sketch1" it's blue sketch
- Whatever plane you decide to choose, press the "Look at Face/Plane/Sketch" icon in the top right hand corner (The person looking at a face)
- This will allow the view to go to the view where you want to sketch on
- Click on "Sketching" which is next to the "Modeling" right above the "Details View"
- Here will be Several Options
  - Draw: This is where you can decide what shape you want to use
  - Modify: This is the extras such as fillets, chamfers and corners
  - Dimensions: This is where you can select what type of dimensions you will be using
  - Constraints: This is where you can constrain lines or connect lines
    - When you want to connect lines together, click on each end and make them "Coincident" this way the shape will connect when you change dimensions
  - Settings: This is where you can show a grid or snap grid
- Sketch Color:
  - Teal: Underdefined: The sketch does not have enough dimensions to constrain and tell the program what exactly the shape is
  - Blue: Defined: The sketch is fully defined and does not need any more dimensions
  - Red: Overdefined: The sketch has repeating dimensions that causes errors
- For this tutorial, draw a circle. I made mine coincident to the middle by pressing the vertex in the middle and one of the axis and then repeat the process with the second axis to center the circle
- Dimensions: The diameter is 2 mm, under dimensions to display the number, click "Display" and then "Value" instead of "name"
- To change the dimensions, the "Details View" in the bottom left hand corner will say D1 and from there you can change the diameter
- From there in order to create the length of the cylinder, press "Extrude" at the top (4th row) towards the right. From there it will ask what geometry, click on your sketch and click "Apply". Make sure the "Operation" is "Add Material" to Extrude.
- Then choose a "Depth" in this case it's 200 mm. Then click "Generate" the lightning bolt next to the "New Sketch" symbol.
- Your cylinder should look like image 1.

5. Return to the project and open the Model tab. With that open, go to the subtab of "Geometry", named "Solid". Under Solid go to "Assignment" under "Material" to assign Fused Silica or whatever material you decide to choose.

6. Go to the "Mesh" tab. In this case the "Element Size" under the "Sizing" tab is 0.04 and the "Relevance Center" as "Fine". Right click on the mesh and press "Generate mesh".

7. Under the Modal tab, go to the Analysis Settings and change the "Max Modes to Find" for ANSYS to calculate. In this tutorial, the amount of modes that were used was 17.

8. Right Click the Modal and press on "Fixed Support". This will make the bar a cantilever bar, once the geometry is set to fix one face of the bar. Press on one of the faces and click on "apply" on the Geometry.

9. Right click on the solution and press "Solve". Let ANSYS run the modes through.

10. On the Solution tab, the "Tabular Data" is listed but the Total Deformation has not been listed. In order to do so, select all the frequency of the modes in the column and right click and press "Create Mode Shape Results".

11. Once loaded, the total deformation will have a lightning bolt next to each entry, right click and press "Solve" or "Evaluate All Results". This will make all the entries have a green check mark.

12. This will give the user the ability to animate each entry. This is down by clicking the play (sideways triangle button). ANSYS will run through the simulation for that mode that is selected, shown in image 2.

13. Using Mathematica (or another computational system) input the analytical solution for a Cantilever bar fixed to one end.

w_n=(k_nL)²Sqrt(EI/mL⁴)
- Where:
- w_n is the frequency measured in radians/second
- E = Young's Modulus
- I = moment of cross section
  - I_rectangle= ba³/12 (b and a are the sides)
  - I_circle = (Pi/64)(d⁴) (d is the diameter)
- m = mass per unit length
- L = length of the bar
- k_n relates to the amount of nodes
  - k₁L = 1.875, k₂L = 4.694, k₃L = 7.855, k₄L = 10.996, k₅L = 14.137
  - n greater than 5: k_nL = (2n -1)(Pi/2)
Convert w_n to f measured in Hz

14. Compare only to the bar actually bending, not twisting or contracting. There are modes that are the same due to the symmetry of the bar. In image 3 the underlined frequencies compare to the analytical calculations (Mathematica) and the computational calculations (ANSYS).

Attachment 1: Simple_Cantilever_200_mm_Long_Geometry.PNG

Attachment 2: Simple_Cantilever_200_mm_Long.PNG

Attachment 3: Comparison_between_ANSYS_and_Calculations_Fused_Silica_200_mm_L.PNG

106

Tue Jun 28 16:54:23 2016

Nikhil Mathur

Ansys 14.5 Indroductory Tutorial: Modal Frequency Convergence

Analysis

This tutorial will go through how to show frequency convergence for a cylindrical cantilever using Ansys 14.5 and Mathematica.

Attachment 1: ConvergenceTutorial.pdf.gz

107

Wed Jun 29 14:14:44 2016

Joy Westland

ANSYS Tutorials with Basic Meshing

Analysis

Here are a series of tutorials for basic meshing principles from ANSYS Meshing Basics:

ANSYS Meshing Fine Mesh Basic Tutorial 1: https://www.youtube.com/watch?v=sZIX3CJkWBE
ANSYS Meshing Method Basic Tutorial 2: https://www.youtube.com/watch?v=ATSnvFUbEk4
ANSYS Meshing Refinement Mesh Basic Tutorial 3: https://www.youtube.com/watch?v=QVfJiydCu2g
ANSYS Meshing Sizing Mesh Basic Tutorial 4: https://www.youtube.com/watch?v=ODJ11YDC6ac
ANSYS Meshing Spheres of Influence Basic Tutorial 5: https://www.youtube.com/watch?v=AQlGccK_X-0
Body of Influnce 6: https://www.youtube.com/watch?v=3E1p1w32jt0
Section Plane 7: https://www.youtube.com/watch?v=hhZOJSESJEU
Mapped and Match Control 8: https://www.youtube.com/watch?v=3pogywR8Vgw
MultiZone and Inflation 9: https://www.youtube.com/watch?v=vxVBvANHuB0
Sizing Soft/Hard 10: https://www.youtube.com/watch?v=D8UzdC5Gmhs

108

Fri Jul 29 14:33:41 2016

Joy Westland

A Tutorial in Importing SolidWorks Files and Applying a Gaussian Force in ANSYS for a LIGO Test Mass

Here is a tutorial in importing SolidWorks into ANSYS and the steps needed to apply a Gaussian Force to the LIGO test mass that’s imported.

Using SolidWorks:

Download the SolidWorks Zip Folders from the DCC
1. https://dcc.ligo.org/login/index.shtml?entityID=https%3A%2F%2Fdcc.ligo.org%2Fshibboleth-sp&return=https%3A%2F%2Fdcc.ligo.org%2FShibboleth.sso%2FLogin%3FSAMLDS%3D1%26target%3Dss%253Amem%253A15b6c314d87e3fa8b3768d89cb6b9836fe39c754 (LIGO-D1000760-v4)
2. Open/export the zip folders into a different file
For only the test mass and ears, open the file called: D0902456 ITM OPTIC WITH EARS ASSEMBLY. This will represent the bottom mass.
An assembly can be imported into ANSYS but it’s easier to convert an assembly into a part before importing it into ANSYS. Also this will allow you to perform a split line.
1. To do this, resave the assembly but before pressing save, change the file to PRT extension instead of Assembly.
Open the PRT file of the test mass, make a new sketch on the face of the test mass.
Draw a circle (Or whatever shape) on the test mass. In this case a 0.1 m circle was made in the middle of the test mass.
From there go to “Insert” and then press “Curve” and then go to “Split Line”. Split line allows a user to project the sketch onto the part. This makes it possible to press the sketch separately from the part. This is a useful tool because in ANSYS, once split line has been used on a sketch, a user can press that shape separately on the face of the object. The importance of this tool allows a user to click on the circle separately and apply a force in that particular area.
1. In “Split Line” press the “sketch” you want to project onto the “face” of the object.

Importing SolidWorks into ANSYS:

Once the part has been made, choose the “static structural analysis”.
In the geometry: Import the test mass that was converted into a part
Once imported, press the geometry again and “edit”
In the edit module, “generate” the part and once the part has loaded notice the circle can be pressed such that it is a different part of the test mass surface.
Exit geometry module

Applying Gaussian Force:

Enter the “model” module to edit the setup of the analysis
Assign the material that you want for the test mass under “Geometry” à “Solid” under the “Material” and “Assignment”
Under the “Coordinate Systems”, make a new coordinate system
“Coordinate System:
1. Click on the face, in this case the circle made on the test mass for the “geometry” and “apply”
2. Under “Definition” à “Type” à Change from Cartesian to Cylindrical. This allows the Gaussian Force to be distributed correctly
Under “Analysis Settings” Turn on “Large Deflection”
Add “gravity” under “Static Structural”
1. Treat the test mass is if it were the bottom mass so make sure gravity is pointing the correct way, such that the wires on the ears would extend upward.
Insert “Fix” to the top surfaces of the ears
Insert “Pressure”
1. Press on the circle made to apply for the pressure
2. Under “Definition” change the “Magnitude” to “Function” (the arrow at the end of the Magnitude entry bar)
3. Once function has been activated: A Gaussian force of: 1/((3.141592654*0.0156^2)*2.718281828^((x/0.0156)^2)) was used in SI units. Note that ANSYS does not use symbols. Once that’s entered into the “Magnitude”, under “Function” the “Coordinate System” will appear. Change that to the coordinate system that was made in step 4 of the cylindrical system.
4. Under “Graph Controls” Make sure that the X-Axis is changed from Time to X.
5. Pick a range for the graph and the number of segments that you want to look at.
“Solve” the system and right click on “Solution” and evaluate the different results you need.

Attachment 1: Bottom_Test_Mass_With_Ears.PNG

Attachment 2: Applying_Parameters.PNG

Attachment 3: Applying_Gaussian_Force.PNG

115

Thu Nov 2 17:23:56 2017

Aaron

Modelling suspension noise

aLIGO Suspensions Toy Model

On Wednesday I started making my own model of the aLIGO suspensions, with the top of the silica fibers attached to ears that are fixed rather attached to an additional suspension stage (so this will be a one stage suspension).

I grabbed the aLIGO ear design from the DCC: LIGO-D080751-v4

I am almost done with the model, should have it working tomorrow and will add it to the experimental gravity github in an appropriate place.

116

Fri Nov 3 15:03:10 2017

Aaron

Modelling suspension noise

Model Geometry

Test Mass

I found the dimension of the test mass flat in the drawings of the mock test mass design here: LIGO-D080687.

Fibers

I modelled the fibers with the profile described in LIGO-D080751, fig 3.7.

Ears

I grabbed the d-values from LIGO-T1000545, but since the d-value is defined as the distance from the center of mass (of the penultimate mass (PUM) or the E/ITM) to the bend point (BP) of the fiber (I believe the point on the fiber with maximal flexure in the fundamental mode), I did not go through the effort of figuring out where the bend point is but rather grabbed the horn-CM distance from LIGO-T1100407

I wanted to get the real aLIGO parameters for the first version of this model, and have parametrized the model in such a way that I can define all of the parameters that need to change (surface area of the ear-TM bond, length of the fibers, thickness and profile of fibers, d-value, etc) and scale them with mass in some way for future iterations on this design.

I need to pare down the number of parameters, because I started by fully defining the ears and now am importing a 3D model of the ears and planning to scale these with mass.

Materials

For the material of the entire test mass and suspension, I used the fused silica that is specified as [solid,NIST SRM 739 - Type I]. I wasn't sure the difference between the types of silica, but this one said SRM so I thought it might have been defined on my distribution of COMSOL by a LIGO person. A quick google search showed me that person may have been rana?? https://labcit.ligo.caltech.edu/~rana/research/etm.html

Physics

I'm using a solid mechanics model.

Fixed Boundary Constraint

I fixed the position of the bonding surfaces for the PUM ears, so it is as if they are contacted to a completely fixed PUM (the PUM is not included in the model, but the upper ears are included, so the constraint is on the ears not the fiber. See drawing).

Gravity

I added gravity to all parts of the model. Apparently, it is not trivial to use gravity in a frequency domain study in COMSOL, as described in this presentation here. Fortunately, the presentation in the link is interested in the transfer function for a mass on a string also, so I follow the simulation steps they describe below.

Boundary Load

I add a boundary load that will vary sinusoidally for the frequency domain study.

Mesh

I have not yet messed with the meshing for these models. Obviously the points with more flexture and smaller parts (like at the horns of the ears, the tapering parts of the fibers, etc) will require a finer mesh.

Study

I need to incorporate the advice on how to build this study described in the link above. The following might also be useful, though I haven't looked through them yet:

https://www.comsol.com/model/dynamics-of-double-pendulum-14021

https://www.comsol.se/forum/thread/4843/pendulum-response?last=2010-04-27T01:48:26Z

117

Wed Nov 15 14:05:12 2017

Aaron

Modelling suspension noise

Model Geometry

I pared down the number of parameters in the model to only the necessary ones. These are the ones that remain:

TM_radius: Radius of the test mass

TM_width: Width of the test mass

TM_flats: length of TM flats

ear_length: length of the ear

horn_spacing: length of the ear

horn_gap: gap between the top of the horn and the TM on the near side

d_val: distance from the CM to the bend point

horn_BP: distance from the horn to the bend point

ear_height_tot_nominal: nominal total height of the ear and horn for the unscaled (aLIGO) design (this name made more sense in a previous version of the model)

fiber_stock_length: length of the fiber's stock

fiber_neck_length: length of the fiber's neck

fiber_thick_length: length of the thick section of the fiber

fiber_main_length: length of the main section of fiber (the thinnest part)

fiber_taper_length: length of the tapering section of fiber

fiber_stock_radius: radius of the fiber stock

fiber_thick_radius: radius of the thick section of fiber

fiber_main_radius: radius of the main section of fiber

F_load: force of the boundary load used for the excitation in the frequency domain study

ear_scale_height: scale the height of the ear

ear_scale_length: scale the length of the ear

ear_scale_width: scale the width of the ear

Materials

Physics

Rana suggests that for the purpose of this study, it is not necessary to actually have COMSOL handle gravity as a restoring force... I'm not sure if I understand why this is yet? It seems that if we are interested in the relative strain energy in different parts of the wire compared to other parts of the system, it is important that the wire be under tension. If we have no gravity, the wire is effectively not under tension.

Mesh

Study

I need to incorporate the advice on how to build this study described in the link above. The following might also be useful, though I haven't looked through them yet:

https://www.comsol.com/model/dynamics-of-double-pendulum-14021

https://www.comsol.se/forum/thread/4843/pendulum-response?last=2010-04-27T01:48:26Z

118

Mon Dec 4 16:27:13 2017

aaron