TM Modal Damping logbook
Dennis Coyne
TM Modal Damping logbook
Exporting with universal files (*.unv)
5/23/2008
Discovered that Hans Bantilan only exported displacement vectors for the modes in
his analysis in support of Parametric Instabilities (PI). [Used vi to search on data set
2414 in the universal file.]
5/24/2008
One can choose to only export results (and not the FEM). This can reduce the model
file considerably if one is exporting multiple modal result runs, where you need the
FEM only exported once. However, filtering the output by use of groups does not
work on data at/on elements and nodes (unfortunately).
The I-Deas project "hbantila" has only a few model files named 7test through 14test.
I tried to open them but do not have permission (within I-Deas) to open them
directly. When I copied 14test.mf1 and 14test.mf2 into my directory
(~coyne/AL/COC/T_modes/hans/), and try to open with I-Deas it says the file is
locked by another. Renaming to test14 allows me to open, but I-Deas says it will be
associated with the project "hbantila" not "coyne". The model file does not have
flats.
test7 has 11,216 nodes, 2560 elements and 10 modes around 28,340 hz
test14 has 19,285 nodes and no results
The modal results files in ~hbantila, i.e. acoustic-f1-f2-flats.unv, where f1 and f2 are
frequency range values, have 21,797 nodes and from the name should have flats in
the optic geometry.
The model file "AL_ITM_modes" in the project "coyne" has flats and 21,797 nodes. It
seems that Hans used my model as is. This model has 100 modes calculated and
saved; 50 starting at 20 kHz and 50 starting at 40 kHz for use in comparing the
modal density to the tesmass5.c analytical formulation.
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Dennis Coyne
5/24/2008
Using drawings available, and some Pro-E CAD models imported into SolidWorks, I
determined the approximate dimensions and location of the ear bonds. The bonds
are tear shaped (D060055-02) with a length of 22 mm and a width of 12.8 mm. The
total surface area is 177.5 mm^2. I'll approximate with a 13 x 22 mm rectangular
area. Using the Noise Prototype ear bonding jig specification (T070156-00) and the
ear bonding jig drawing (D070391-01), as well as the silica test mass drawing
(D040431-C), I was able to determine the nominal position of the two bond areas on
each flat.
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Dennis Coyne
The existing I-Deas FEM ("AL_ITM_modes") has a single 15 x 18 mm region
segmented in the solid model underlying the mesh clearly intended to represent the
bond area.
5/25/2008
Copied the existing geometry in model file "AL_ITM_modes", named "ETM-ITM 2", to
"ETM-ITM 3" as a starting point to build the new geometry for the new FEM. Tried to
edit the creation history to move the partitioning planes to new locaitons (per the
sketch of 5/24) but couldn't figure out how to get this functionality to work. So I
deleted the partitioning steps back to just a cylinder with flats and vertical and
horizontal planes which cleave the solid. I then partitioned the solid per the sketch of
5/24 to create defined regions for the bonded ears.
I set the wedge angle (was zero in Hans Bantilan's & Bill Kell's model) to 0.08 deg
horizontal, with the minimum thickness equal (theoretically) to 200 mm. Thickness
at one flat is 200.0095 mm and 200.4652 mm at the other flat. The ear bond areas
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Dennis Coyne
are referenced from the face that is normal to the cylindrical axis (nominally the AR
surface).
The bevel has not been included in the model.
The CP ESD mask (D080177-00) has an inner radius of 133 mm. I'll use this as an
approximate inner radius of the influence of the ESD on the TM for partitioning. To
permit determination of whether higher azimuthal levels of segmentation in the ESD
pattern will improve the overlap, and controllability, of higher order acoustic modes,
I partitioned into 8 sectors.
5/25/2008
I was/am concerned that Han's FEM may not be fine enough (converged) to calculate
~100 kHz modes with much accuracy. The highest mod that I calculated with this
model was 42 kHz. It seems adequate (by eye) to capture these spatial gradients
(parabolic elements).
INSERT MODAL PLOTS HERE
5/25/2008
Fused Silica property data: The FEM used by Hans has the following properties:
E = 70.0 GPa
 = 0.17
G = 29.9 GPa
 = 2201 kg/m^3
Strigin, Blair et. al. (P080057-00) use:
E = 73.1 GPa
 = 0.17
 = 2203 kg/m^3
One Heraeus source:
http://www.siltec.ru/leaflets/Base-Materials.pdf
Lists
E = 70.0 GPa
 = 0.17
 = 2201 kg/m^3
But it si a leaflet and not a tech data sheet for any one particular grade of glass. I
can't seem to find any more definitive data for Heraeus FS.
Corning HPFS data sheets have:
E = 72.7 GPa
 = 0.16
 = 2201 kg/m^3
Other web sources have elastic modulus values more similar to Corning's. For
example, Schott Lithotec:
http://www.unitedlens.com/stuff/contentmgr/files/226b47c5d575a0530afcf452700c7
315/misc/fused_silica_us.pdf
E = 72 GPa
 = 0.17
 = 2.2 g/cm^3
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Dennis Coyne
A direct measurement of the elastic modulus and Poisson's ratio for Heraeus fused
silica in this reference:
Comte C., Von Stebut J.
Microprobe-type measurement of Young's modulus and Poisson coefficient
by means of depth sensing indentation and acoustic microscopy
(2002) Surface and Coatings Technology, 154 (1), pp. 42-48.
yields:
E = 72.9 GPa
 = 0.17
So I will use the following property data in the FEM:
E = 72.9 GPa
 = 0.17
 = 2201 kg/m^3
5/25/2008
Meshing & FEA setup
fem1: I thought (think) that a mapped mesh with symmetry would give more
accurate mode splitting. So I spent close to an hour manually setting parameters for
the 140 volumes created by the partitioning referred to above. However some of the
volumes did not mesh -- the routine failed. In addition, it became clear to me that by
segmenting azimuthally I created converging triangular surfaces (volumes) which
tend to concentrate element size (or cause aspect ratio problems). While this
concentration toward the center is appropriate for Gaussian loading (e.g. the Levin
approach for thermal noise calculations) it is not well suited for higher order acoustic
mode calculation.
fem2: So, I resorted to a free mesh:
20 mm element length, free mesh
21,830 nodes
14,623 parabolic, tetrahedron elements
Started run to calculate 1 mode > 10 Hz and store displacement, stress, strain and
strain energy to get some measure of the time to calculate the mode, but more
importantly a determination of whether the strain energy exported into the *.unv file
is correct or not. If it is correct then I don't need to export stress or strain.
The run took about 14 minutes wall clock time.
The first mode frequency is 5946 Hz with a modal mass of 11.76 kg. (The total mess
mass is 39.63 Kg). Compare to 5971 Hz for a right circular cylinder of the nominal
dimensions calculated with:
0.728e12 /* Youngs modulus for SiO2 */
0.17 /* Poisson ratio for SiO2 */
2.196 /* density of SiO2 (gm/cc) */
5/25/2008
Plots of the strain energy don't look correct by eye. Plots of stress and strain look
reasonable. Defined element and node groups for all canonical surfaces (HR, AR,
barrel, ear bond areas). Exported the results and model to
AL_TM_model3_fem2_mode1.unv (32.7 MB)
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The file size is large because stress and strain is written at each node of each
element -- there are a lot of repeated nodes.
Displacement: 21,830 x 6 values = 131k
Stress: 14,623 x 10 nodes x 6 values = 877k
Strain like stress
Strain energy 14,623 x 1 value? = 15k?
I then deleted the result set (to clear strain energy and stress results for mode 1)
and set to run and calculate 25 modes and store displacement and strain. I estimate
that the resulting *.unv file will be ~500MB.
5/27/2008
Run ran without errors. From the *.lis file the run took 47 minutes wall clock time to
calculate the first 25 modes (with displacement and strain saved).
I exported just the results (not the FEM) to a *.unv file. The file is 353MB in size. So,
using the modal density fit:
upper freq
Hz
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
#
modes
58
165
346
614
981
1459
2057
2785
3651
FEA
hrs
1.82
5.17
10.83
19.23
30.74
45.70
64.44
87.25
114.41
*.unv files
TB
0.820
2.329
4.881
8.667
13.853
20.596
29.039
39.317
51.559
5/26/2008
Extended uffread.m to be able to read strain results from the *.unv file.
Verified that stress is related to strain in accordance with the isotropic elastic tensor
– still have some ambiguity with regard to the order of the stress and strain terms in
the “symmetric global tensor” order output by I-Deas in the *.unv file.
5/27-28/2008
Investigating FEM convergence: Ran the fem2 model (21,830 nodes and 14,623
parabolic, tetrahedron elements) for the 1st 25 modes > 40 kHz. Frequencies do not
match those calculated with the FEM Hans used (see plot below). The run took about
54 minutes wall clock time.
fem3: Created a model with 49,593 nodes and 34,074 parabolic, tetrahedron
elements). Started a recalculation of the 1st 25 modes > 40 kHz. The run took 9.5
hrs wall clock time. A comparison of the frequencies between the models is given in
the table & figure below. The frequencies seem to match to ~0.5%. In addition to
frequency convergence, should also check strain energy convergence, but first need
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Dennis Coyne
to calculate strain energies from strain field (and verify the strain energy output from
I-Deas).
AL ITM Modal Frequency
450
400
y = 5E-10x2.5727
Cummulative number of Modes
350
300
250
200
150
100
50
0
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
Frequency (Hz)
testmass5.c
FEA,1st 25
FEA, 50 > 20 kHz
FEA, 50 > 40 kHz
FEA,1st 25 > 40kHz
Power (testmass5.c)
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Dennis Coyne
compare fem2 & fem3
41200
41000
frequency (Hz)
40800
40600
fem3
fem2
hans
40400
40200
40000
39800
330
335
340
345
350
355
360
365
mode number
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Dennis Coyne
page 9 of 27
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Dennis Coyne
5/28/2008
Wrote out the results only (no FEM) for fem3 (25 modes > 40 kHz) – created a
849MB *.unv file with displacement, strain and strain energy results.
5/28/2008
I used the first mode results, exported to a *.unv file, to calculate the strain energy
density and strain energy.
Here is the calculated strain energy (ergs) for each element on the AR face of the
optic.
Compare to the strain energy for calculated by I-Deas for the AR face, when
corrected by division by the shear modulus (E/(2 (1+)):
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Dennis Coyne
The results are basically identical. I don’t have any idea why the strain energy would
be multiplied by the shear modulus. The non-smooth, non-monotonic nature of the
strain energy (high apparent spatial frequency) is due to the fact that this is strain
energy integrated over each element and the element sizes vary quite a bit.
Compare to the calculated energy density:
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Dennis Coyne
Also compare to the strain energy density calculated (by dividing by the element
volumes as calculated from the nodal positions) from the element strain energy in
the I-Deas *.unv file and corrected by division by the shear modulus:
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Dennis Coyne
This is an encouraging development, since calculating the strain energy from the
strain field is cumbersome with the *.unv output (since it is given at each of the 10
to 20 nodes per element, depending upon element formulation). However, the
torsional strain component dominates in the strain energy for this first mode (as is
apparent from the strain energy plots given below). This may be the reason that
dividing by the shear modulus basically corrects the strain energy results in the
*.unv file for *this* mode only, i.e. mode dominated by other stress terms may need
to be divided by other terms in the global stiffness matrix for a three-dimensional,
isotropic material:

 1
 

1  
 

C   E 1    1  
1   1  2  








1
1 
1
1 

1

1
1  2
2(1   )
1  2
2(1   )












1  2 
2(1   ) 
Or,
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TM Modal Damping logbook
  2 
 

 
C   





Dennis Coyne


  2

  2










 
Where the Lame constants are related to the Young’s modulus, E, and the shear
modulus, G, as follows:
E
2(1   )
E

(1   )(1  2 )
 G
Looking at the difference between:
(a) the strain energy density calculated output from I-Deas (in the *.unv file,
corrected by division by G and multiplied by the element volumes as
determined from the nodal positions), and
(b) the strain energy density calculated from the stress and strain fields in the IDeas *.unv file (using just an average for the nodes of each element and not
using an integral based on the element interpolation function)
gives the following result:
The differences are not small (~2/80) and are systematic, not random. The largest
differences occur at the perimeter of the AR face where the non-torsional strains are
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Dennis Coyne
more important; It seems I need to look at (an)other mode shape with non-torsional
strain to see if the “correction” by dividing by G applies universally, or not.
Just for completeness, here are plots of strain components:
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Dennis Coyne
5/29/2008
So I need to look at a few other modes. In preparation for this task, I merged Matt
Evan’s uffread.m changes (to reduce memory requirements and increase speed) with
my changes and tested it on the single first mode *.unv file (for the results given
above).
I read the first 25 modes from the file AL_ITM_1st25modes_disp_strain.unv (345
MB, model 3, fem2) using the revised uffread.m code with just displacement and
strain output in the unv file. Saved the workspace to
AL_ITM_1st25modes_disp_strain.mat (170 MB). Unfortunately there isn’t any I-Deas
exported strain energy results to compare to calculated strain energy. In addition to
save file space, I didn’t export the FEM data so there is no nodal or element or group
data (which could be exported from another *.unv file … but what a bother.)
frequency(1) = 5946.11 Hz, Modal Mass = 11.7614 Kg
frequency(2) = 6062.25 Hz, Modal Mass = 11.1825 Kg
frequency(3) = 8199.16 Hz, Modal Mass = 14.9996 Kg
frequency(4) = 8260.23 Hz, Modal Mass = 36.3103 Kg
frequency(5) = 8316.29 Hz, Modal Mass = 18.2511 Kg
frequency(6) = 9107.35 Hz, Modal Mass = 10.1229 Kg
frequency(7) = 9363.39 Hz, Modal Mass = 9.74137 Kg
frequency(8) = 9383.4 Hz, Modal Mass = 8.36256 Kg
frequency(9) = 9819.9 Hz, Modal Mass = 10.7852 Kg
frequency(10) = 9873.88 Hz, Modal Mass = 14.3484 Kg
frequency(11) = 10211.6 Hz, Modal Mass = 8.84046 Kg
frequency(12) = 10445 Hz, Modal Mass = 8.55771 Kg
frequency(13) = 10461.3 Hz, Modal Mass = 24.5955 Kg
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TM Modal Damping logbook
frequency(14)
frequency(15)
frequency(16)
frequency(17)
frequency(18)
frequency(19)
frequency(20)
frequency(21)
frequency(22)
frequency(23)
frequency(24)
frequency(25)
Dennis Coyne
=
=
=
=
=
=
=
=
=
=
=
=
12578.3
12602.2
12685.3
12696.7
12806.6
12919.7
13004.9
13022.4
13057.3
13197.9
13267.5
14179.5
Hz,
Hz,
Hz,
Hz,
Hz,
Hz,
Hz,
Hz,
Hz,
Hz,
Hz,
Hz,
Modal
Modal
Modal
Modal
Modal
Modal
Modal
Modal
Modal
Modal
Modal
Modal
Mass
Mass
Mass
Mass
Mass
Mass
Mass
Mass
Mass
Mass
Mass
Mass
=
=
=
=
=
=
=
=
=
=
=
=
6.23122 Kg
10.9904 Kg
13.066 Kg
5.77222 Kg
5.05712 Kg
5.58889 Kg
5.12666 Kg
3.91994 Kg
5.47909 Kg
15.4358 Kg
9.40098 Kg
6.0878 Kg
Also I should compare the strain energy values in the *.unv file with the screen
values from I-Deas – these are the values that I’ve quoted in the past. Which
reminds me – there is a caution in my notes (LOOK IT UP!) that one must switch
on/off a particular parameter when asking for strain energy on the screen or one
gets incorrect values. Perhaps the *.unv file has this ‘flavor’ of incorrect strain
energy values.
5/29-30/2008
Given the uncertainties in the I-Deas FEA strain energy and the very real possibility
of the need to calculate the strain energies from strain data which is a
computationally intensive job (especially is properly calculated using the element
interpolation functions for accuracy), I decided to explore doing the calculation with
Ansys.
Found out (again) that we do not have the SolidWorks model importer/converter for
Ansys (at least on the engineering workstation, 4 processor, 64 bit machine) – we
really need to get this option. Must convert to a standard CAD file format first – step
works (maybe best).
Created a SolidWorks model of the ITM/ETM with flats and 0.08 deg wedge (no
bevel). Defined reference geometry (planes and sketches) for use with the
insert/feature/slices tool to partition the solid into multiple bodies.
Imported the geometry into Ansys running on deneb (using remote desktop from
home). The connection or the system was exceedingly slow. Had to terminate before
saving. Will repeat when on the CIT LAN.
5/30/2008
Finally got Ansys workbench to work – sort of:
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Next step is to use an Ansys command to effectively join the bodies into a single part
(forgot the command name). This should still retain the separate bodies but ensures
continuity of the mesh at the mating surfaces.
Had lots of problems running with Windows Remote Desktop. Had to reduce screen
size to 640 x 480 to run reliably and with any speed. Incredibly small screen – not
practical.
6/1/2008
Running Ansys on my desktop machine, I found I could import the geometry directly
from SolidWorks. Ran the modal analysis for just the 1st mode. Took 5 min and 12
sec on my desktop machine (3.39 GHz single processor, 3.25 GB RAM).
45,182 nodes
20,710 elements
5943 Hz, modal mass ?
Butterfly mode (curious – I thought I-Deas showed a torsional motion
in addition to the butterfly bending motion)
Have discovered to my severe disappointment that strain energy results are only
available in a (static) structural analysis in Ansys WorkBench (and then only in ver.
11.0 released in Sep 2007). Looks like a dead end for Ansys, unless “Classic Ansys”
(not the workbench) has the capability to calculate modal strain energy.
Took quite a while to discover that the way one apparently takes a model from Ansys
WorkBench to “classic” Ansys is to highlight the “solution” object in the ‘tree’, then
select “tools, write ansys input file …”. When I ran the model imported into Ansys it
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Dennis Coyne
popped up a message that 2 warnings were generated (but didn’t tell me what they
were) and then popped up another 1 warning message. In both cases I elected to
proceed with the analysis. Calculation of the 1st mode took ~5 minutes and had the
same frequency as for Ansys WorkBench. The contour plots of displacement and Von
Mises strain looked to be the same as for Ansys WorkBench. When I tried to plot
strain energy density, a message popped up that indicated that the elastic strain
energy density (SEND) was not available. I could plot the element strain energy
(funny looking because of the variable element volumes). According to the manual
SOLID186 and SOLID187 elements should have SEND available (or at least the
manual did not preclude these results explicitly for a modal analysis). Should call
technical support and ask I suppose.
6/2/2008
Finally got Comsol installed. (One doesn’t install/import the license file – one points
to port 1718 of rigel.ligo.caltech.edu.)
Comsol imports just two flavors of CAD (at least with the translators that we have) -*.stl and *.wrl (VRML). I exported both from the SolidWorks geometry which is
partitioned with the regions that I wish to calculate strain energy from.
Comsol failed to import the *.wrl file. Gave 2 warnings:
VRML file contains 1216 triangles.
Warning: There are 459 duplicated triangles.
Warning: There are 31 singular triangles.
And then a fatal error: can’t parameterize face.
Comsol did import the *.stl file, but with one warning:
STL file contains 1968 triangles.
Number of points after snapping: 711
Warning: There are 53 duplicated triangles.
Partitioned triangles into 265 faces.
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Note the peculiarities in the imported geometry.
When I tried to mesh the 1 subdomain, I get an error:
An empty cavity was generated
Failed to insert point
- x coordinate: 186.371
- y coordinate: 151.071
- z coordinate: 78.5
Sigh … guess I’ll try generating the geometry within Comsol.
Created a solid model using 3D primatives and Boolean composite creation, including
flats and wedge angle:
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Does not yet have interior boundaries (or surface boundaries) to represent the
surface patches where I’d like to get strain energy and modal displacements (i.e. ear
bond areas and ESD pattern areas), but it’s a start.
Used the free mesh option with “fine” which generated the following mesh with
15,067 elements:
Tried to calculate the first mode on my laptop (while running other tasks: email, MS
word, browser, adobe acrobat) and after 12 min Comsol stopped – out of memory.
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However I was monitoring the memory use and it did not seem to have hit the
machine max.
Saved this mesh as mesh 0 and re-meshed (mesh 1) with “normal” instead of “fine”.
Generated 7,766 elements.
Ran in about 3 minutes. Calculated first frequency as 5944 Hz. Mode shape
(displacement):
Strain energy density!! … but why is the amplitude so high (3E+13)? Makes me
wonder if I-Deas is correct and I’m wrong about dividing by G – CHECK AGAIN!
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Subdomain integration of the strain energy density:
Value of integral: 7.667782e10 [J], Expression: Ws_smsld, Subdomain:
all
Now I need to export the data. In order to directly export to Matlab, one launches
Matlab from within Comsol (file, client/server/Matlab, connect to Matlab …) and then
exports (file, export, FEM structure …).
>> fem
fem =
version:
appl:
geom:
mesh:
frame:
shape:
gporder:
cporder:
border:
units:
equ:
bnd:
edg:
pnt:
var:
elemmph:
draw:
lib:
ode:
xmesh:
sol:
[1x1 struct]
{[1x1 struct]}
[1x1 solid3]
[1x1 struct]
{'ref'}
[1x1 struct]
[1x1 struct]
[1x1 struct]
1
[1x1 struct]
[1x1 struct]
[1x1 struct]
[1x1 struct]
[1x1 struct]
{1x8 cell}
{[1x1 struct] [1x1 struct]}
[1x1 struct]
[1x1 struct]
[1x1 struct]
[1x1 com.femlab.xmesh.Xmesh]
[1x1 femsol]
>> fem.sol
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ans =
u: [34767x1 double]
lambda: 0 -3.7346e+004i
eigname: 'lambda'
>> abs(fem.sol.lambda)/2/pi
ans =
5.9438e+003
>> fem.sol.u
??? Undefined function or method 'flgetarray' for input
arguments of type
'int32'.
Error in ==> flexchprop>l_flgetmatrix at 53
vao = flgetarray(exch.getDim,exch.getAdr,exch.isReal);
Error in ==> flexchprop at 21
[varargout{1:nout}] = l_flgetmatrix(outprop, outstr);
Error in ==> femsol.subsref at 30
out(:,i)=flexchprop('flgetmatrix',prop,STR);
>>
As far as I can tell this should work! Sigh …
I used the “file, export, postprocessing data …” capability to write out a text file with
strain energy density results with the “coordinates, data” option at node points. The
file has 77,660 lines of {x,y,z,sed}, i.e. 7,766 tetrahedral elements x 10 nodes per
element. File size is 7.7 MB.
Note that while exiting Comsol, it asked if I’d like to save the model. I indicated yes,
it indicated a fatal error. Sigh …
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