Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

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Daniel.Walia
Posts: 19
Joined: Thu Dec 15, 2016 7:56 am
Organization: University of Rostock
Location: Germany

Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

Postby Daniel.Walia » Wed Jan 30, 2019 9:25 am

Dear Jason, (or maybe others who are experienced in this topic),

i am currently setting up an OpenFAST (v2.0) (i´ll call it OFAST below) model of the NREL 5.0MW reference turbine on a TLP floater. We did series of tank tests (wave and wind) using a physical 1:50 scale model of our TLP and a respective
5 MW NREL turbine. The scaled turbine was provided by the tank test facility. Due to limitations in scaling the 1:50 model of the NREL 5MW used in the tank tests differed in COG, stiffness, masses, etc. from ideal values. This is why we have
to adjust several parameters of the NREL 5MW turbine used in the OFAST simulation, to better comply with the physical model.
While altering distances, mass distribution and so on is not a very demanding task, it drove us into some uncertainties when setting up BModes(JJ), to calculate the modeshapes of the tower of the physical model (upscaled by factor of 50).

From what I have read here in the forum in the input file of BModesJJ the stiffness/damping of the subsystem has to be taken into account. So FAST or OFAST or to be more specific, ElastoDyn expects the user to provide mode shapes not of the tower itself but rather the mode shapes of the tower-support-structure-system so the restraints of the support-structure have to be considered here.

This is why 4 matrices have to be defined and this is the point where I am getting confused a bit. We are using Ansys AQWA as we do not have WAMIT available. So I am confused with the denotation of at least one of the matrices:

1. Platform mass inertia 3X3 matrix (i_matrix_pform)
This is easy to be found by determining the inertial properties of the support structure in any 3D-CAD tool

2. Platform-reference-point-referred hydrodynamic 6X6 matrix (hydro_M)
I have no clue which matrix exactly this one should be. Is this the frequency dependent added mass matrix? If no, could you please tell me which matrix this is in the description of the OC3 Definition? Or this one might by also elucidated in the HydroDyn User´s Guide and Theory Manual?

3. Platform-reference-point-referred hydrodynamic 6X6 stiffness matrix (hydro_K)
Just for the sake of completeness. The hydrodynamic stiffness matrix is denoted in the OC3 Definition as C^(Hydrostatic)_(ij)

4. Mooring-system 6X6 stiffness matrix (mooring_K)
You have determined the mooring stiffness matrix by use of MAP als described in the OC3 Defnition. We have set up our model by use of MoorDyn tool instead of MAP. I think MoorDyn does not output the mooring stiffness matrix. So I have to use MAP at this point, is that correct?

Finally one general question with regard to the hydrodynamic preprocessing for BModes. You have allways used WAMIT to preprocess hydro_M and hydro_K. Wouldn´ t it be also possible to distinguish these matrices by the use of HydroDyn when only using Morison´s approach at this point?

Thank you,
and kind regards.

Daniel

Jason.Jonkman
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Location: Boulder, CO
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Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

Postby Jason.Jonkman » Wed Jan 30, 2019 2:43 pm

Dear Daniel,

Here are my answers to your questions:

1) Correct.

2) For hydro_M, you could use the hydrodynamic added mass from WAMIT (or in your case, AQWA) at a given frequency e.g. the zero-frequency limit.

3) C^Hydrostatic_ij in the OC3-Hywind specification report only includes the buoyancy-related restoring; the body weight-related restoring is not included om C^Hydrostatic_ij, but should be included in the platform stiffness specified in BModes--see the following forum topic for more information: viewtopic.php?f=4&t=742&p=2826.

4) Correct, MoorDyn cannot currently export the mooring stiffness matrix. You could use MAP++ or an equivalent tool to derive this.

5) Without modification of the source code, HydroDyn cannot directly output the 6x6 added-mass matrix associated with strip-theory (Morison) members. And HydroDyn does not intrinsically form the 6x6 hydrostatic restoring matrix for strip-theory members, but instead, this restoring matrix is specified via the 6c6 AddCLin matrix input to HydroDyn.

I hope that helps.

Best regards
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Daniel.Walia
Posts: 19
Joined: Thu Dec 15, 2016 7:56 am
Organization: University of Rostock
Location: Germany

Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

Postby Daniel.Walia » Mon Feb 04, 2019 7:55 am

Dear Jason,
thank you for your explanations. They made most of the topics clear to me. However, the following question remains:

Jason.Jonkman wrote:2) For hydro_M, you could use the hydrodynamic added mass from WAMIT (or in your case, AQWA) at a given frequency e.g. the zero-frequency limit.
[

I have tried to find out more about the zero- or infinte-frequency limit but wasn´t successfull here. Could you please help me understanding what the zero- r infinite-frequency limit in this context means? Or maybe there is a textbook, or paper you could refer to, to help me understand what this is about. Otherwise of course, choosing the added mass closed the eigenfrequency of the structure would also make sense. Am I correct here, when assuming that here only the eigenfrequency of the substructure itself is of importance and tower, RNA, and tendons should be neglected for estimating the correct eigenfrequency in order to determine the correct added mass for BModes?

Kind regards,
Daniel

Jason.Jonkman
Posts: 4224
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

Postby Jason.Jonkman » Mon Feb 04, 2019 12:31 pm

Dear Daniel,

Hydrodynamic added mass is in reality frequency dependent. BModes, however, requires that you specify added mass as a fixed value and it will derive all support structure natural frequencies from this fixed value of the added mass. It would be most accurate if you iterate at each eigenfrequency calculated by BModes to ensure that you are using the added mass associated with that frequency as input. But this would take a bit of effort and is not something I have done myself. Instead, what I've done is just pick the added mass at one frequency (e.g. at zero or infinite frequency) and assume that the eigenfrequencies calculated by BModes are not strongly sensitivity to the frequency dependence of added mass. I originally said "zero-frequency limit) because my understanding is that WAMIT solves different equations when calculating the added mass when the frequency is zero or infinite than what WAMIT solves when calculating the added mass at other frequencies between these limits.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Daniel.Walia
Posts: 19
Joined: Thu Dec 15, 2016 7:56 am
Organization: University of Rostock
Location: Germany

Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

Postby Daniel.Walia » Thu Feb 07, 2019 6:55 am

Dear Jason,

thank you very much for your explanation. I think this made everything pretty much clear to me. I ran into an issue with an Segmentation Fault error, when trying to run the model by using MAP++ in order to derive the mooring stiffness matrix. But this is a different issue. That is why I created a topic on github. https://github.com/OpenFAST/openfast/issues/238.

Kind regards,
Daniel

Daniel.Walia
Posts: 19
Joined: Thu Dec 15, 2016 7:56 am
Organization: University of Rostock
Location: Germany

Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

Postby Daniel.Walia » Wed Jul 03, 2019 3:36 am

Dear Jason,

I have defined all matrices in the BModes_JJ input file to define the flexible substructure:

Code: Select all

Platform-reference-point-referred hydrodynamic 6X6 matrix (hydro_M):
6.2094E+06  -2.5740E+03 -2.7409E+02 -6.3934E+04 -1.1295E+08 -1.1394E+04
-2.4698E+03  6.2098E+06  6.7063E+01  1.1296E+08  7.0010E+04  1.3278E+04
6.7882E+02  4.1912E+02  5.3607E+06  3.2493E+04  -3.6474E+04  -1.2128E+04
-4.9645E+04  1.1283E+08  2.1984E+04 3.3288E+09  1.5005E+06  3.3540E+05
-1.1283E+08  6.3898E+04  -1.2112E+04  1.6855E+06  3.3288E+09 2.7344E+05
-1.3890E+04  1.4809E+04  -7.8033E+03  3.6008E+05  2.7383E+05  2.6467E+09
Platform-reference-point-referred hydrodynamic 6X6 stiffness matrix (hydro_K):
0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   2.7955E+05   5.0874E+02   -4.8518E+02   0.0000E+00
0.0000E+00   0.0000E+00   5.0874E+02   -1.7924E+09   -1.1335E+02   -1.8099E+01
0.0000E+00   0.0000E+00   -4.8518E+02   -1.1335E+02   -1.7924E+09   -4.8314E+01
0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00   0.0000E+00
Mooring-system 6X6 stiffness matrix (mooring_K):
2.63e+06    -1.61e-10     0.00e+00    -2.47e-09    -8.06e+07     0.00e+00
0.00e+00     2.63e+06     0.00e+00     8.06e+07     0.00e+00     0.00e+00
2.99e+03     0.00e+00     5.10e+07     0.00e+00    -9.19e+04     0.00e+00
-8.04e-23     8.06e+06    -9.13e-03     1.39e+10    -3.28e-12    -7.05e-11
-8.06e+06     4.94e-10     1.86e-02    -2.74e-01     1.39e+10     3.22e-04
2.98e-06     1.31e-06     2.30e-02    -2.49e-01    -2.55e-01     1.26e+08


Hereby I get the tower frequencies and mode shapes as an output from BModes_JJ:

Code: Select all

          tower frequencies & mode shapes
            --- only first  20 modes printed


 -------- Mode No.   1  (freq = 0.210229E-01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000    0.000000    0.000000   -0.009381   -0.005859    0.000003
 0.0200    0.000000    0.000000   -0.009544   -0.010430    0.000003
 0.0400    0.000000    0.000000   -0.009798   -0.014932    0.000003
 0.0600    0.000000    0.000000   -0.010141   -0.019367    0.000003
 0.0800    0.000000   -0.000001   -0.010572   -0.023734    0.000003
 0.1000    0.000000   -0.000001   -0.011090   -0.028033    0.000003
 0.1200    0.000000   -0.000001   -0.011693   -0.032264    0.000003
 0.1400    0.000000   -0.000001   -0.012380   -0.036428    0.000003
 0.1600    0.000000   -0.000001   -0.013150   -0.040524    0.000003
 0.1800    0.000000   -0.000001   -0.014000   -0.044553    0.000003
 0.2000    0.000000   -0.000001   -0.014931   -0.048514    0.000003
 0.2200    0.000000   -0.000001   -0.015941   -0.052407    0.000003
 0.2400    0.000000   -0.000001   -0.017027   -0.056232    0.000003
 0.2600    0.000000   -0.000002   -0.018189   -0.059990    0.000003
 0.2800    0.000000   -0.000002   -0.019426   -0.063680    0.000003
 0.3000    0.000000   -0.000002   -0.020736   -0.067302    0.000003
 0.3200    0.000000   -0.000002   -0.022118   -0.070857    0.000003
 0.3400    0.000000   -0.000002   -0.023570   -0.074345    0.000003
 0.3600    0.000000   -0.000002   -0.025091   -0.077764    0.000003
 0.3800    0.000000   -0.000002   -0.026680   -0.081116    0.000003
 0.4000    0.000000   -0.000002   -0.028335   -0.084401    0.000003
 0.4200    0.000000   -0.000003   -0.030056   -0.087618    0.000003
 0.4400    0.000000   -0.000003   -0.031840   -0.090767    0.000003
 0.4600   -0.000001   -0.000003   -0.033686   -0.093849    0.000003
 0.4800   -0.000001   -0.000003   -0.035593   -0.096863    0.000003
 0.5000   -0.000001   -0.000003   -0.037560   -0.099810    0.000003
 0.5200   -0.000001   -0.000003   -0.039585   -0.102689    0.000003
 0.5400   -0.000001   -0.000003   -0.041667   -0.105501    0.000003
 0.5600   -0.000001   -0.000003   -0.043805   -0.108245    0.000003
 0.5800   -0.000001   -0.000003   -0.045996   -0.110922    0.000003
 0.6000   -0.000001   -0.000003   -0.048241   -0.113532    0.000003
 0.6200   -0.000001   -0.000003   -0.050537   -0.116074    0.000003
 0.6400   -0.000001   -0.000003   -0.052884   -0.118549    0.000003
 0.6600   -0.000001   -0.000003   -0.055279   -0.120956    0.000003
 0.6800   -0.000001   -0.000004   -0.057721   -0.123294    0.000003
 0.7000   -0.000001   -0.000004   -0.060210   -0.125562    0.000003
 0.7200   -0.000001   -0.000004   -0.062744   -0.127751    0.000003
 0.7400   -0.000001   -0.000004   -0.065321   -0.129844    0.000003
 0.7600   -0.000002   -0.000004   -0.067940   -0.131788    0.000003
 0.7800   -0.000002   -0.000004   -0.070599   -0.133448    0.000003
 0.8000   -0.000002   -0.000004   -0.073297   -0.134474    0.000003
 0.8200   -0.000002   -0.000004   -0.076032   -0.134009    0.000003
 0.8400   -0.000002   -0.000004   -0.078799   -0.130053    0.000003
 0.8600   -0.000002   -0.000004   -0.081594   -0.118284    0.000003
 0.8800   -0.000002   -0.000004   -0.084409   -0.090332    0.000003
 0.9000   -0.000002   -0.000004   -0.087236   -0.032826    0.000003
 0.9200   -0.000002   -0.000004   -0.090084    0.067413    0.000003
 0.9400   -0.000002   -0.000004   -0.093012    0.199716    0.000003
 0.9600   -0.000002   -0.000004   -0.096158    0.277842    0.000003
 0.9800   -0.000002   -0.000004   -0.099562    0.127479    0.000003
 1.0000   -0.000002   -0.000004   -0.102155   -0.152659    0.000003


 -------- Mode No.   2  (freq = 0.733419E-01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.001248   -0.000006    0.047381    0.000639    0.000001
 0.0200   -0.001250   -0.000149    0.047449    0.006171    0.000002
 0.0400   -0.001254   -0.000289    0.047627    0.011583    0.000003
 0.0600   -0.001261   -0.000425    0.047912    0.016877    0.000004
 0.0800   -0.001271   -0.000559    0.048301    0.022052    0.000005
 0.1000   -0.001283   -0.000690    0.048793    0.027109    0.000006
 0.1200   -0.001298   -0.000818    0.049385    0.032048    0.000008
 0.1400   -0.001316   -0.000943    0.050074    0.036869    0.000009
 0.1600   -0.001336   -0.001064    0.050859    0.041573    0.000010
 0.1800   -0.001359   -0.001183    0.051736    0.046160    0.000011
 0.2000   -0.001383   -0.001299    0.052704    0.050630    0.000012
 0.2200   -0.001411   -0.001412    0.053761    0.054984    0.000014
 0.2400   -0.001440   -0.001522    0.054903    0.059222    0.000015
 0.2600   -0.001471   -0.001630    0.056129    0.063344    0.000016
 0.2800   -0.001505   -0.001734    0.057436    0.067351    0.000017
 0.3000   -0.001541   -0.001835    0.058822    0.071243    0.000018
 0.3200   -0.001579   -0.001934    0.060285    0.075020    0.000020
 0.3400   -0.001618   -0.002030    0.061822    0.078683    0.000021
 0.3600   -0.001660   -0.002122    0.063432    0.082232    0.000022
 0.3800   -0.001703   -0.002212    0.065111    0.085668    0.000023
 0.4000   -0.001748   -0.002299    0.066858    0.088990    0.000024
 0.4200   -0.001795   -0.002384    0.068670    0.092200    0.000025
 0.4400   -0.001843   -0.002465    0.070545    0.095298    0.000027
 0.4600   -0.001894   -0.002544    0.072481    0.098284    0.000028
 0.4800   -0.001945   -0.002619    0.074475    0.101159    0.000029
 0.5000   -0.001998   -0.002692    0.076526    0.103922    0.000030
 0.5200   -0.002053   -0.002763    0.078632    0.106576    0.000031
 0.5400   -0.002109   -0.002830    0.080789    0.109119    0.000033
 0.5600   -0.002166   -0.002895    0.082996    0.111553    0.000034
 0.5800   -0.002225   -0.002957    0.085250    0.113879    0.000035
 0.6000   -0.002284   -0.003016    0.087550    0.116096    0.000036
 0.6200   -0.002345   -0.003072    0.089893    0.118205    0.000037
 0.6400   -0.002407   -0.003126    0.092277    0.120206    0.000039
 0.6600   -0.002470   -0.003177    0.094701    0.122100    0.000040
 0.6800   -0.002534   -0.003225    0.097161    0.123884    0.000041
 0.7000   -0.002599   -0.003271    0.099656    0.125555    0.000042
 0.7200   -0.002665   -0.003314    0.102183    0.127097    0.000043
 0.7400   -0.002732   -0.003355    0.104741    0.128470    0.000044
 0.7600   -0.002799   -0.003392    0.107327    0.129568    0.000046
 0.7800   -0.002867   -0.003428    0.109939    0.130124    0.000047
 0.8000   -0.002936   -0.003460    0.112574    0.129496    0.000048
 0.8200   -0.003006   -0.003490    0.115229    0.126233    0.000049
 0.8400   -0.003076   -0.003518    0.117898    0.117330    0.000050
 0.8600   -0.003147   -0.003543    0.120577    0.097368    0.000052
 0.8800   -0.003218   -0.003565    0.123262    0.058833    0.000053
 0.9000   -0.003289   -0.003585    0.125963   -0.002422    0.000054
 0.9200   -0.003361   -0.003603    0.128723   -0.069979    0.000055
 0.9400   -0.003433   -0.003618    0.131607   -0.083108    0.000056
 0.9600   -0.003506   -0.003630    0.134523    0.024952    0.000057
 0.9800   -0.003578   -0.003641    0.137132    0.142883    0.000059
 1.0000   -0.003651   -0.003649    0.139856    0.138381    0.000060


 -------- Mode No.   3  (freq = 0.796251E-01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000003   -0.000001   -0.010352    0.009274   -0.000003
 0.0200   -0.000003   -0.000001   -0.010125    0.013391   -0.000003
 0.0400   -0.000003   -0.000001   -0.009816    0.017455   -0.000003
 0.0600   -0.000003   -0.000001   -0.009427    0.021464   -0.000003
 0.0800   -0.000003   -0.000001   -0.008958    0.025421   -0.000003
 0.1000   -0.000003   -0.000001   -0.008411    0.029323   -0.000003
 0.1200   -0.000003   -0.000002   -0.007786    0.033171   -0.000003
 0.1400   -0.000003   -0.000002   -0.007084    0.036965   -0.000003
 0.1600   -0.000003   -0.000002   -0.006307    0.040704   -0.000003
 0.1800   -0.000003   -0.000002   -0.005456    0.044389   -0.000003
 0.2000   -0.000003   -0.000002   -0.004532    0.048019   -0.000003
 0.2200   -0.000003   -0.000002   -0.003536    0.051595   -0.000003
 0.2400   -0.000003   -0.000002   -0.002469    0.055115   -0.000003
 0.2600   -0.000004   -0.000002   -0.001332    0.058580   -0.000003
 0.2800   -0.000004   -0.000003   -0.000126    0.061990   -0.000003
 0.3000   -0.000004   -0.000003    0.001148    0.065345   -0.000003
 0.3200   -0.000004   -0.000003    0.002488    0.068644   -0.000003
 0.3400   -0.000004   -0.000003    0.003893    0.071887   -0.000003
 0.3600   -0.000004   -0.000003    0.005363    0.075074   -0.000003
 0.3800   -0.000004   -0.000003    0.006896    0.078206   -0.000003
 0.4000   -0.000004   -0.000003    0.008491    0.081281   -0.000003
 0.4200   -0.000004   -0.000003    0.010146    0.084300   -0.000003
 0.4400   -0.000004   -0.000003    0.011862    0.087262   -0.000003
 0.4600   -0.000004   -0.000003    0.013637    0.090168   -0.000003
 0.4800   -0.000004   -0.000003    0.015468    0.093017   -0.000003
 0.5000   -0.000004   -0.000003    0.017357    0.095809   -0.000003
 0.5200   -0.000004   -0.000003    0.019300    0.098544   -0.000003
 0.5400   -0.000004   -0.000003    0.021298    0.101222   -0.000003
 0.5600   -0.000004   -0.000003    0.023349    0.103842   -0.000003
 0.5800   -0.000004   -0.000003    0.025452    0.106406   -0.000003
 0.6000   -0.000005   -0.000003    0.027605    0.108911   -0.000003
 0.6200   -0.000005   -0.000003    0.029808    0.111359   -0.000003
 0.6400   -0.000005   -0.000003    0.032059    0.113748   -0.000003
 0.6600   -0.000005   -0.000004    0.034357    0.116080   -0.000003
 0.6800   -0.000005   -0.000004    0.036702    0.118351   -0.000003
 0.7000   -0.000005   -0.000004    0.039091    0.120561   -0.000003
 0.7200   -0.000005   -0.000004    0.041524    0.122700   -0.000003
 0.7400   -0.000005   -0.000004    0.044000    0.124750   -0.000003
 0.7600   -0.000005   -0.000004    0.046516    0.126652   -0.000003
 0.7800   -0.000005   -0.000004    0.049073    0.128262   -0.000003
 0.8000   -0.000005   -0.000004    0.051668    0.129200   -0.000003
 0.8200   -0.000005   -0.000004    0.054299    0.128539   -0.000003
 0.8400   -0.000005   -0.000004    0.056963    0.124121   -0.000003
 0.8600   -0.000006   -0.000004    0.059653    0.111273   -0.000003
 0.8800   -0.000006   -0.000004    0.062363    0.080946   -0.000003
 0.9000   -0.000006   -0.000004    0.065084    0.018679   -0.000003
 0.9200   -0.000006   -0.000004    0.067825   -0.089791   -0.000003
 0.9400   -0.000006   -0.000004    0.070650   -0.232965   -0.000003
 0.9600   -0.000006   -0.000004    0.073711   -0.317607   -0.000003
 0.9800   -0.000006   -0.000004    0.077048   -0.155104   -0.000003
 1.0000   -0.000006   -0.000004    0.079508    0.147858   -0.000003


 -------- Mode No.   4  (freq = 0.796251E-01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000003   -0.000001   -0.010352    0.009274   -0.000003
 0.0200   -0.000003   -0.000001   -0.010125    0.013391   -0.000003
 0.0400   -0.000003   -0.000001   -0.009816    0.017455   -0.000003
 0.0600   -0.000003   -0.000001   -0.009427    0.021464   -0.000003
 0.0800   -0.000003   -0.000001   -0.008958    0.025421   -0.000003
 0.1000   -0.000003   -0.000001   -0.008411    0.029323   -0.000003
 0.1200   -0.000003   -0.000002   -0.007786    0.033171   -0.000003
 0.1400   -0.000003   -0.000002   -0.007084    0.036965   -0.000003
 0.1600   -0.000003   -0.000002   -0.006307    0.040704   -0.000003
 0.1800   -0.000003   -0.000002   -0.005456    0.044389   -0.000003
 0.2000   -0.000003   -0.000002   -0.004532    0.048019   -0.000003
 0.2200   -0.000003   -0.000002   -0.003536    0.051595   -0.000003
 0.2400   -0.000003   -0.000002   -0.002469    0.055115   -0.000003
 0.2600   -0.000004   -0.000002   -0.001332    0.058580   -0.000003
 0.2800   -0.000004   -0.000003   -0.000126    0.061990   -0.000003
 0.3000   -0.000004   -0.000003    0.001148    0.065345   -0.000003
 0.3200   -0.000004   -0.000003    0.002488    0.068644   -0.000003
 0.3400   -0.000004   -0.000003    0.003893    0.071887   -0.000003
 0.3600   -0.000004   -0.000003    0.005363    0.075074   -0.000003
 0.3800   -0.000004   -0.000003    0.006896    0.078206   -0.000003
 0.4000   -0.000004   -0.000003    0.008491    0.081281   -0.000003
 0.4200   -0.000004   -0.000003    0.010146    0.084300   -0.000003
 0.4400   -0.000004   -0.000003    0.011862    0.087262   -0.000003
 0.4600   -0.000004   -0.000003    0.013637    0.090168   -0.000003
 0.4800   -0.000004   -0.000003    0.015468    0.093017   -0.000003
 0.5000   -0.000004   -0.000003    0.017357    0.095809   -0.000003
 0.5200   -0.000004   -0.000003    0.019300    0.098544   -0.000003
 0.5400   -0.000004   -0.000003    0.021298    0.101222   -0.000003
 0.5600   -0.000004   -0.000003    0.023349    0.103842   -0.000003
 0.5800   -0.000004   -0.000003    0.025452    0.106406   -0.000003
 0.6000   -0.000005   -0.000003    0.027605    0.108911   -0.000003
 0.6200   -0.000005   -0.000003    0.029808    0.111359   -0.000003
 0.6400   -0.000005   -0.000003    0.032059    0.113748   -0.000003
 0.6600   -0.000005   -0.000004    0.034357    0.116080   -0.000003
 0.6800   -0.000005   -0.000004    0.036702    0.118351   -0.000003
 0.7000   -0.000005   -0.000004    0.039091    0.120561   -0.000003
 0.7200   -0.000005   -0.000004    0.041524    0.122700   -0.000003
 0.7400   -0.000005   -0.000004    0.044000    0.124750   -0.000003
 0.7600   -0.000005   -0.000004    0.046516    0.126652   -0.000003
 0.7800   -0.000005   -0.000004    0.049073    0.128262   -0.000003
 0.8000   -0.000005   -0.000004    0.051668    0.129200   -0.000003
 0.8200   -0.000005   -0.000004    0.054299    0.128539   -0.000003
 0.8400   -0.000005   -0.000004    0.056963    0.124121   -0.000003
 0.8600   -0.000006   -0.000004    0.059653    0.111273   -0.000003
 0.8800   -0.000006   -0.000004    0.062363    0.080946   -0.000003
 0.9000   -0.000006   -0.000004    0.065084    0.018679   -0.000003
 0.9200   -0.000006   -0.000004    0.067825   -0.089791   -0.000003
 0.9400   -0.000006   -0.000004    0.070650   -0.232965   -0.000003
 0.9600   -0.000006   -0.000004    0.073711   -0.317607   -0.000003
 0.9800   -0.000006   -0.000004    0.077048   -0.155104   -0.000003
 1.0000   -0.000006   -0.000004    0.079508    0.147858   -0.000003


 -------- Mode No.   5  (freq = 0.896226E-01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000266    0.000275   -0.013231    0.014583   -0.000001
 0.0200   -0.000260    0.000370   -0.012888    0.019639   -0.000001
 0.0400   -0.000251    0.000463   -0.012446    0.024594   -0.000002
 0.0600   -0.000241    0.000554   -0.011905    0.029449   -0.000003
 0.0800   -0.000229    0.000644   -0.011268    0.034203   -0.000004
 0.1000   -0.000215    0.000731   -0.010538    0.038856   -0.000005
 0.1200   -0.000200    0.000817   -0.009715    0.043408   -0.000006
 0.1400   -0.000183    0.000901   -0.008802    0.047860   -0.000007
 0.1600   -0.000164    0.000984   -0.007801    0.052210   -0.000008
 0.1800   -0.000143    0.001064   -0.006714    0.056459   -0.000009
 0.2000   -0.000121    0.001142   -0.005543    0.060607   -0.000009
 0.2200   -0.000098    0.001219   -0.004291    0.064653   -0.000010
 0.2400   -0.000073    0.001294   -0.002958    0.068598   -0.000011
 0.2600   -0.000046    0.001367   -0.001547    0.072442   -0.000012
 0.2800   -0.000018    0.001438   -0.000061    0.076185   -0.000013
 0.3000    0.000012    0.001507    0.001499    0.079826   -0.000014
 0.3200    0.000042    0.001575    0.003131    0.083365   -0.000015
 0.3400    0.000075    0.001640    0.004833    0.086804   -0.000016
 0.3600    0.000108    0.001704    0.006603    0.090140   -0.000017
 0.3800    0.000143    0.001766    0.008438    0.093376   -0.000017
 0.4000    0.000179    0.001826    0.010337    0.096510   -0.000018
 0.4200    0.000216    0.001884    0.012298    0.099544   -0.000019
 0.4400    0.000254    0.001940    0.014318    0.102476   -0.000020
 0.4600    0.000293    0.001995    0.016396    0.105307   -0.000021
 0.4800    0.000334    0.002048    0.018530    0.108038   -0.000022
 0.5000    0.000375    0.002098    0.020717    0.110668   -0.000023
 0.5200    0.000418    0.002147    0.022956    0.113198   -0.000024
 0.5400    0.000461    0.002195    0.025244    0.115627   -0.000025
 0.5600    0.000505    0.002240    0.027580    0.117957   -0.000025
 0.5800    0.000551    0.002283    0.029962    0.120186   -0.000026
 0.6000    0.000597    0.002325    0.032387    0.122317   -0.000027
 0.6200    0.000644    0.002365    0.034854    0.124348   -0.000028
 0.6400    0.000691    0.002403    0.037360    0.126281   -0.000029
 0.6600    0.000740    0.002439    0.039905    0.128116   -0.000030
 0.6800    0.000789    0.002473    0.042484    0.129855   -0.000031
 0.7000    0.000839    0.002506    0.045098    0.131502   -0.000032
 0.7200    0.000889    0.002537    0.047743    0.133069   -0.000032
 0.7400    0.000940    0.002566    0.050418    0.134586   -0.000033
 0.7600    0.000992    0.002593    0.053122    0.136129   -0.000034
 0.7800    0.001044    0.002619    0.055851    0.137891   -0.000035
 0.8000    0.001097    0.002642    0.058606    0.140329   -0.000036
 0.8200    0.001150    0.002664    0.061385    0.144475   -0.000037
 0.8400    0.001203    0.002685    0.064188    0.152449   -0.000038
 0.8600    0.001257    0.002703    0.067015    0.168024   -0.000039
 0.8800    0.001311    0.002720    0.069866    0.196286   -0.000040
 0.9000    0.001366    0.002735    0.072729    0.239483   -0.000040
 0.9200    0.001421    0.002749    0.075568    0.284509   -0.000041
 0.9400    0.001476    0.002761    0.078338    0.286667   -0.000042
 0.9600    0.001531    0.002771    0.081111    0.201555   -0.000043
 0.9800    0.001587    0.002779    0.084140    0.123445   -0.000044
 1.0000    0.001642    0.002786    0.087039    0.144930   -0.000045


 -------- Mode No.   6  (freq = 0.285658E+00 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000367   -0.000475    0.020390    0.026464    0.000000
 0.0200   -0.000377   -0.000440    0.020900    0.024568   -0.000002
 0.0400   -0.000385   -0.000404    0.021372    0.022646   -0.000004
 0.0600   -0.000393   -0.000367    0.021806    0.020700   -0.000006
 0.0800   -0.000400   -0.000330    0.022200    0.018731   -0.000008
 0.1000   -0.000406   -0.000293    0.022555    0.016743   -0.000011
 0.1200   -0.000411   -0.000255    0.022870    0.014737   -0.000013
 0.1400   -0.000416   -0.000217    0.023144    0.012715   -0.000015
 0.1600   -0.000420   -0.000179    0.023378    0.010680   -0.000017
 0.1800   -0.000423   -0.000141    0.023571    0.008634   -0.000019
 0.2000   -0.000426   -0.000102    0.023723    0.006578   -0.000021
 0.2200   -0.000427   -0.000063    0.023834    0.004516   -0.000023
 0.2400   -0.000428   -0.000024    0.023904    0.002449   -0.000026
 0.2600   -0.000428    0.000015    0.023932    0.000381   -0.000028
 0.2800   -0.000428    0.000054    0.023919   -0.001688   -0.000030
 0.3000   -0.000426    0.000093    0.023865   -0.003754   -0.000032
 0.3200   -0.000424    0.000132    0.023769   -0.005816   -0.000034
 0.3400   -0.000421    0.000170    0.023632   -0.007871   -0.000036
 0.3600   -0.000417    0.000209    0.023454   -0.009916   -0.000038
 0.3800   -0.000413    0.000248    0.023236   -0.011950   -0.000041
 0.4000   -0.000407    0.000286    0.022976   -0.013970   -0.000043
 0.4200   -0.000401    0.000324    0.022677   -0.015974   -0.000045
 0.4400   -0.000394    0.000362    0.022338   -0.017960   -0.000047
 0.4600   -0.000387    0.000399    0.021959   -0.019926   -0.000049
 0.4800   -0.000378    0.000436    0.021541   -0.021869   -0.000051
 0.5000   -0.000369    0.000473    0.021084   -0.023788   -0.000053
 0.5200   -0.000359    0.000509    0.020589   -0.025680   -0.000056
 0.5400   -0.000349    0.000545    0.020057   -0.027544   -0.000058
 0.5600   -0.000338    0.000580    0.019488   -0.029378   -0.000060
 0.5800   -0.000326    0.000614    0.018882   -0.031179   -0.000062
 0.6000   -0.000313    0.000648    0.018241   -0.032945   -0.000064
 0.6200   -0.000300    0.000682    0.017565   -0.034676   -0.000066
 0.6400   -0.000286    0.000714    0.016854   -0.036368   -0.000068
 0.6600   -0.000271    0.000746    0.016110   -0.038019   -0.000071
 0.6800   -0.000256    0.000778    0.015333   -0.039623   -0.000073
 0.7000   -0.000240    0.000808    0.014525   -0.041167   -0.000075
 0.7200   -0.000224    0.000838    0.013686   -0.042620   -0.000077
 0.7400   -0.000207    0.000867    0.012816   -0.043898   -0.000079
 0.7600   -0.000189    0.000895    0.011918   -0.044785   -0.000081
 0.7800   -0.000171    0.000922    0.010993   -0.044739   -0.000083
 0.8000   -0.000152    0.000949    0.010043   -0.042445   -0.000086
 0.8200   -0.000133    0.000975    0.009073   -0.034914   -0.000088
 0.8400   -0.000113    0.000999    0.008088   -0.015860   -0.000090
 0.8600   -0.000093    0.001023    0.007099    0.026354   -0.000092
 0.8800   -0.000072    0.001046    0.006112    0.108872   -0.000094
 0.9000   -0.000051    0.001068    0.005107    0.244855   -0.000096
 0.9200   -0.000029    0.001089    0.004001    0.410167   -0.000099
 0.9400   -0.000007    0.001109    0.002649    0.490391   -0.000101
 0.9600    0.000015    0.001129    0.001154    0.328216   -0.000103
 0.9800    0.000038    0.001147    0.000113    0.051373   -0.000105
 1.0000    0.000061    0.001165   -0.000793   -0.058879   -0.000107


 -------- Mode No.   7  (freq = 0.291687E+00 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000    0.000092    0.000123    0.050167    0.064829   -0.000001
 0.0200    0.000094    0.000114    0.051405    0.058954    0.000000
 0.0400    0.000096    0.000105    0.052525    0.053061    0.000000
 0.0600    0.000098    0.000096    0.053528    0.047152    0.000001
 0.0800    0.000100    0.000087    0.054412    0.041235    0.000001
 0.1000    0.000102    0.000078    0.055177    0.035314    0.000002
 0.1200    0.000103    0.000068    0.055824    0.029395    0.000003
 0.1400    0.000104    0.000059    0.056353    0.023484    0.000003
 0.1600    0.000106    0.000049    0.056764    0.017585    0.000004
 0.1800    0.000106    0.000040    0.057056    0.011705    0.000004
 0.2000    0.000107    0.000030    0.057232    0.005850    0.000005
 0.2200    0.000108    0.000020    0.057291    0.000024    0.000005
 0.2400    0.000108    0.000010    0.057233   -0.005766    0.000006
 0.2600    0.000108    0.000000    0.057060   -0.011514    0.000007
 0.2800    0.000108   -0.000010    0.056773   -0.017216    0.000007
 0.3000    0.000108   -0.000020    0.056372   -0.022864    0.000008
 0.3200    0.000107   -0.000029    0.055859   -0.028454    0.000008
 0.3400    0.000106   -0.000039    0.055234   -0.033980    0.000009
 0.3600    0.000106   -0.000049    0.054500   -0.039436    0.000009
 0.3800    0.000104   -0.000059    0.053657   -0.044817    0.000010
 0.4000    0.000103   -0.000069    0.052708   -0.050118    0.000011
 0.4200    0.000102   -0.000079    0.051653   -0.055333    0.000011
 0.4400    0.000100   -0.000088    0.050495   -0.060457    0.000012
 0.4600    0.000098   -0.000098    0.049236   -0.065485    0.000012
 0.4800    0.000096   -0.000107    0.047876   -0.070412    0.000013
 0.5000    0.000094   -0.000117    0.046420   -0.075233    0.000013
 0.5200    0.000092   -0.000126    0.044868   -0.079943    0.000014
 0.5400    0.000089   -0.000135    0.043223   -0.084538    0.000015
 0.5600    0.000086   -0.000144    0.041487   -0.089014    0.000015
 0.5800    0.000083   -0.000153    0.039663   -0.093365    0.000016
 0.6000    0.000080   -0.000162    0.037753   -0.097589    0.000016
 0.6200    0.000077   -0.000170    0.035760   -0.101682    0.000017
 0.6400    0.000073   -0.000179    0.033687   -0.105639    0.000017
 0.6600    0.000070   -0.000187    0.031536   -0.109458    0.000018
 0.6800    0.000066   -0.000195    0.029310   -0.113137    0.000018
 0.7000    0.000062   -0.000203    0.027011   -0.116676    0.000019
 0.7200    0.000058   -0.000211    0.024644   -0.120083    0.000020
 0.7400    0.000053   -0.000218    0.022211   -0.123382    0.000020
 0.7600    0.000049   -0.000226    0.019714   -0.126642    0.000021
 0.7800    0.000044   -0.000233    0.017156   -0.130043    0.000021
 0.8000    0.000040   -0.000240    0.014541   -0.134029    0.000022
 0.8200    0.000035   -0.000246    0.011871   -0.139632    0.000022
 0.8400    0.000030   -0.000253    0.009145   -0.149077    0.000023
 0.8600    0.000025   -0.000259    0.006365   -0.166660    0.000024
 0.8800    0.000019   -0.000265    0.003530   -0.199275    0.000024
 0.9000    0.000014   -0.000271    0.000647   -0.254161    0.000025
 0.9200    0.000008   -0.000276   -0.002255   -0.328620    0.000025
 0.9400    0.000003   -0.000282   -0.005118   -0.389331    0.000026
 0.9600   -0.000003   -0.000287   -0.007926   -0.370392    0.000026
 0.9800   -0.000009   -0.000292   -0.010823   -0.256733    0.000027
 1.0000   -0.000014   -0.000296   -0.014019   -0.150609    0.000028


 -------- Mode No.   8  (freq = 0.386050E+00 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000    0.000001    0.000002    0.000108    0.000135    0.000000
 0.0200    0.000001    0.000002    0.000110    0.000055    0.000002
 0.0400    0.000001    0.000002    0.000110   -0.000024    0.000004
 0.0600    0.000001    0.000003    0.000109   -0.000101    0.000006
 0.0800    0.000001    0.000003    0.000106   -0.000177    0.000008
 0.1000    0.000001    0.000003    0.000102   -0.000253    0.000010
 0.1200    0.000001    0.000003    0.000096   -0.000327    0.000012
 0.1400    0.000001    0.000003    0.000089   -0.000400    0.000014
 0.1600    0.000002    0.000004    0.000080   -0.000471    0.000016
 0.1800    0.000002    0.000004    0.000070   -0.000542    0.000018
 0.2000    0.000002    0.000004    0.000058   -0.000611    0.000020
 0.2200    0.000002    0.000004    0.000045   -0.000678    0.000022
 0.2400    0.000002    0.000004    0.000031   -0.000745    0.000024
 0.2600    0.000002    0.000004    0.000016   -0.000810    0.000026
 0.2800    0.000002    0.000004   -0.000001   -0.000874    0.000028
 0.3000    0.000002    0.000003   -0.000019   -0.000937    0.000030
 0.3200    0.000002    0.000003   -0.000039   -0.000998    0.000032
 0.3400    0.000002    0.000003   -0.000059   -0.001058    0.000034
 0.3600    0.000002    0.000003   -0.000081   -0.001117    0.000036
 0.3800    0.000002    0.000003   -0.000104   -0.001175    0.000038
 0.4000    0.000002    0.000002   -0.000128   -0.001231    0.000040
 0.4200    0.000002    0.000002   -0.000153   -0.001286    0.000042
 0.4400    0.000002    0.000002   -0.000179   -0.001340    0.000044
 0.4600    0.000002    0.000001   -0.000207   -0.001393    0.000046
 0.4800    0.000002    0.000001   -0.000235   -0.001444    0.000048
 0.5000    0.000002    0.000001   -0.000264   -0.001495    0.000050
 0.5200    0.000003    0.000000   -0.000295   -0.001544    0.000052
 0.5400    0.000003    0.000000   -0.000326   -0.001593    0.000054
 0.5600    0.000002   -0.000001   -0.000359   -0.001640    0.000056
 0.5800    0.000002   -0.000001   -0.000392   -0.001686    0.000058
 0.6000    0.000002   -0.000001   -0.000426   -0.001732    0.000060
 0.6200    0.000002   -0.000002   -0.000461   -0.001777    0.000062
 0.6400    0.000002   -0.000002   -0.000497   -0.001823    0.000064
 0.6600    0.000002   -0.000003   -0.000534   -0.001869    0.000066
 0.6800    0.000002   -0.000003   -0.000572   -0.001921    0.000068
 0.7000    0.000002   -0.000003   -0.000610   -0.001988    0.000070
 0.7200    0.000002   -0.000004   -0.000650   -0.002098    0.000072
 0.7400    0.000002   -0.000004   -0.000690   -0.002329    0.000074
 0.7600    0.000002   -0.000005   -0.000732   -0.002878    0.000076
 0.7800    0.000002   -0.000005   -0.000776   -0.004247    0.000078
 0.8000    0.000002   -0.000005   -0.000823   -0.007648    0.000080
 0.8200    0.000002   -0.000006   -0.000875   -0.015843    0.000082
 0.8400    0.000002   -0.000006   -0.000940   -0.034628    0.000084
 0.8600    0.000001   -0.000007   -0.001023   -0.074715    0.000086
 0.8800    0.000001   -0.000007   -0.001130   -0.151815    0.000088
 0.9000    0.000001   -0.000007   -0.001241   -0.277746    0.000090
 0.9200    0.000001   -0.000008   -0.001278   -0.429513    0.000092
 0.9400    0.000001   -0.000008   -0.001107   -0.500679    0.000094
 0.9600    0.000001   -0.000008   -0.000828   -0.347408    0.000096
 0.9800    0.000001   -0.000009   -0.000998   -0.095045    0.000098
 1.0000    0.000000   -0.000009   -0.001282   -0.002695    0.000100


 -------- Mode No.   9  (freq = 0.683978E+00 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000057   -0.000067    0.002990    0.003540   -0.000001
 0.0200   -0.000057    0.000032    0.003005   -0.001962   -0.000003
 0.0400   -0.000056    0.000125    0.002914   -0.007136   -0.000004
 0.0600   -0.000052    0.000213    0.002722   -0.011979   -0.000006
 0.0800   -0.000047    0.000294    0.002437   -0.016491   -0.000008
 0.1000   -0.000040    0.000370    0.002065   -0.020670   -0.000010
 0.1200   -0.000032    0.000439    0.001612   -0.024515   -0.000012
 0.1400   -0.000023    0.000503    0.001086   -0.028024   -0.000014
 0.1600   -0.000012    0.000561    0.000494   -0.031198   -0.000015
 0.1800    0.000000    0.000612   -0.000159   -0.034035   -0.000017
 0.2000    0.000012    0.000658   -0.000866   -0.036536   -0.000019
 0.2200    0.000026    0.000697   -0.001619   -0.038700   -0.000021
 0.2400    0.000040    0.000730   -0.002411   -0.040529   -0.000023
 0.2600    0.000055    0.000758   -0.003237   -0.042023   -0.000025
 0.2800    0.000070    0.000779   -0.004090   -0.043185   -0.000026
 0.3000    0.000086    0.000795   -0.004963   -0.044016   -0.000028
 0.3200    0.000102    0.000804   -0.005849   -0.044518   -0.000030
 0.3400    0.000118    0.000808   -0.006741   -0.044695   -0.000032
 0.3600    0.000134    0.000806   -0.007634   -0.044550   -0.000034
 0.3800    0.000150    0.000798   -0.008521   -0.044088   -0.000036
 0.4000    0.000166    0.000784   -0.009396   -0.043311   -0.000037
 0.4200    0.000182    0.000765   -0.010252   -0.042226   -0.000039
 0.4400    0.000197    0.000741   -0.011083   -0.040837   -0.000041
 0.4600    0.000211    0.000711   -0.011883   -0.039152   -0.000043
 0.4800    0.000225    0.000676   -0.012647   -0.037175   -0.000045
 0.5000    0.000238    0.000635   -0.013368   -0.034913   -0.000047
 0.5200    0.000251    0.000590   -0.014041   -0.032375   -0.000048
 0.5400    0.000262    0.000540   -0.014661   -0.029566   -0.000050
 0.5600    0.000272    0.000485   -0.015222   -0.026496   -0.000052
 0.5800    0.000281    0.000425   -0.015719   -0.023172   -0.000054
 0.6000    0.000289    0.000361   -0.016148   -0.019603   -0.000056
 0.6200    0.000296    0.000293   -0.016502   -0.015798   -0.000058
 0.6400    0.000301    0.000220   -0.016778   -0.011764   -0.000059
 0.6600    0.000304    0.000144   -0.016971   -0.007510   -0.000061
 0.6800    0.000307    0.000064   -0.017077   -0.003043   -0.000063
 0.7000    0.000307   -0.000020   -0.017092    0.001637   -0.000065
 0.7200    0.000306   -0.000108   -0.017012    0.006545   -0.000067
 0.7400    0.000303   -0.000198   -0.016832    0.011734   -0.000069
 0.7600    0.000298   -0.000292   -0.016550    0.017360   -0.000070
 0.7800    0.000291   -0.000389   -0.016162    0.023830   -0.000072
 0.8000    0.000282   -0.000489   -0.015662    0.032131   -0.000074
 0.8200    0.000271   -0.000591   -0.015047    0.044507   -0.000076
 0.8400    0.000259   -0.000696   -0.014308    0.065615   -0.000078
 0.8600    0.000244   -0.000803   -0.013438    0.103872   -0.000080
 0.8800    0.000226   -0.000912   -0.012432    0.170982   -0.000081
 0.9000    0.000207   -0.001024   -0.011307    0.273515   -0.000083
 0.9200    0.000185   -0.001137   -0.010130    0.386290   -0.000085
 0.9400    0.000162   -0.001252   -0.009002    0.415407   -0.000087
 0.9600    0.000135   -0.001369   -0.007785    0.256655   -0.000089
 0.9800    0.000107   -0.001488   -0.005955    0.079616   -0.000091
 1.0000    0.000076   -0.001608   -0.004155    0.089888   -0.000092


 -------- Mode No.  10  (freq = 0.772557E+00 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000    0.000004    0.000005   -0.008858   -0.010440    0.000001
 0.0200    0.000004    0.000002   -0.008855    0.010474    0.000001
 0.0400    0.000004    0.000000   -0.008448    0.030080    0.000001
 0.0600    0.000004   -0.000002   -0.007661    0.048373    0.000001
 0.0800    0.000004   -0.000004   -0.006522    0.065346    0.000001
 0.1000    0.000004   -0.000005   -0.005056    0.080995    0.000001
 0.1200    0.000004   -0.000007   -0.003291    0.095315    0.000001
 0.1400    0.000004   -0.000009   -0.001252    0.108304    0.000001
 0.1600    0.000003   -0.000010    0.001033    0.119960    0.000001
 0.1800    0.000003   -0.000012    0.003537    0.130283    0.000001
 0.2000    0.000003   -0.000013    0.006235    0.139275    0.000001
 0.2200    0.000003   -0.000014    0.009099    0.146939    0.000001
 0.2400    0.000002   -0.000015    0.012104    0.153280    0.000001
 0.2600    0.000002   -0.000016    0.015222    0.158306    0.000001
 0.2800    0.000002   -0.000017    0.018427    0.162026    0.000001
 0.3000    0.000001   -0.000018    0.021694    0.164452    0.000001
 0.3200    0.000001   -0.000018    0.024997    0.165599    0.000001
 0.3400    0.000001   -0.000019    0.028310    0.165482    0.000001
 0.3600    0.000000   -0.000019    0.031608    0.164121    0.000001
 0.3800    0.000000   -0.000019    0.034867    0.161536    0.000001
 0.4000    0.000000   -0.000019    0.038061    0.157750    0.000001
 0.4200   -0.000001   -0.000019    0.041169    0.152789    0.000001
 0.4400   -0.000001   -0.000019    0.044165    0.146680    0.000001
 0.4600   -0.000002   -0.000019    0.047028    0.139455    0.000001
 0.4800   -0.000002   -0.000018    0.049736    0.131144    0.000001
 0.5000   -0.000002   -0.000018    0.052267    0.121781    0.000001
 0.5200   -0.000003   -0.000017    0.054601    0.111402    0.000001
 0.5400   -0.000003   -0.000016    0.056717    0.100044    0.000001
 0.5600   -0.000003   -0.000015    0.058596    0.087748    0.000001
 0.5800   -0.000004   -0.000014    0.060221    0.074551    0.000001
 0.6000   -0.000004   -0.000013    0.061573    0.060498    0.000001
 0.6200   -0.000004   -0.000012    0.062635    0.045629    0.000001
 0.6400   -0.000004   -0.000010    0.063393    0.029989    0.000001
 0.6600   -0.000004   -0.000009    0.063830    0.013621    0.000001
 0.6800   -0.000005   -0.000007    0.063933   -0.003429    0.000001
 0.7000   -0.000005   -0.000006    0.063688   -0.021115    0.000001
 0.7200   -0.000005   -0.000004    0.063084   -0.039391    0.000001
 0.7400   -0.000005   -0.000002    0.062109   -0.058203    0.000001
 0.7600   -0.000005    0.000000    0.060752   -0.077487    0.000001
 0.7800   -0.000005    0.000002    0.059003   -0.097143    0.000001
 0.8000   -0.000005    0.000004    0.056855   -0.116983    0.000001
 0.8200   -0.000005    0.000006    0.054299   -0.136611    0.000001
 0.8400   -0.000005    0.000009    0.051329   -0.155158    0.000001
 0.8600   -0.000004    0.000011    0.047940   -0.170797    0.000001
 0.8800   -0.000004    0.000014    0.044130   -0.180030    0.000001
 0.9000   -0.000004    0.000016    0.039895   -0.177314    0.000001
 0.9200   -0.000004    0.000019    0.035228   -0.157236    0.000001
 0.9400   -0.000003    0.000021    0.030099   -0.124307    0.000001
 0.9600   -0.000003    0.000024    0.024447   -0.114146    0.000001
 0.9800   -0.000002    0.000027    0.018253   -0.198183    0.000001
 1.0000   -0.000002    0.000029    0.011954   -0.335470    0.000001


 -------- Mode No.  11  (freq = 0.894703E+00 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000002   -0.000003   -0.005639   -0.006617   -0.000001
 0.0200   -0.000002   -0.000002   -0.005592    0.011107   -0.000001
 0.0400   -0.000002   -0.000001   -0.005202    0.027657   -0.000001
 0.0600   -0.000002   -0.000001   -0.004494    0.043029   -0.000001
 0.0800   -0.000002    0.000000   -0.003489    0.057217   -0.000001
 0.1000   -0.000002    0.000000   -0.002213    0.070219   -0.000001
 0.1200   -0.000002    0.000001   -0.000688    0.082031   -0.000001
 0.1400   -0.000002    0.000002    0.001060    0.092653   -0.000001
 0.1600   -0.000002    0.000002    0.003010    0.102083   -0.000001
 0.1800   -0.000002    0.000003    0.005136    0.110325   -0.000001
 0.2000   -0.000002    0.000003    0.007415    0.117382   -0.000001
 0.2200   -0.000002    0.000004    0.009823    0.123260   -0.000001
 0.2400   -0.000002    0.000004    0.012337    0.127967   -0.000001
 0.2600   -0.000002    0.000005    0.014934    0.131513   -0.000001
 0.2800   -0.000002    0.000005    0.017590    0.133912    0.000000
 0.3000   -0.000001    0.000005    0.020283    0.135178    0.000000
 0.3200   -0.000001    0.000006    0.022990    0.135329    0.000000
 0.3400   -0.000001    0.000006    0.025689    0.134386    0.000000
 0.3600   -0.000001    0.000006    0.028358    0.132371    0.000000
 0.3800   -0.000001    0.000007    0.030977    0.129311    0.000000
 0.4000   -0.000001    0.000007    0.033524    0.125231    0.000000
 0.4200   -0.000001    0.000007    0.035980    0.120164    0.000000
 0.4400   -0.000001    0.000007    0.038324    0.114142    0.000000
 0.4600    0.000000    0.000007    0.040539    0.107199    0.000000
 0.4800    0.000000    0.000007    0.042606    0.099372    0.000000
 0.5000    0.000000    0.000007    0.044508    0.090701    0.000000
 0.5200    0.000000    0.000007    0.046229    0.081226    0.000000
 0.5400    0.000000    0.000007    0.047752    0.070990    0.000000
 0.5600    0.000000    0.000006    0.049064    0.060037    0.000000
 0.5800    0.000000    0.000006    0.050149    0.048413    0.000000
 0.6000    0.000000    0.000006    0.050996    0.036164    0.000000
 0.6200    0.000001    0.000006    0.051592    0.023338    0.000000
 0.6400    0.000001    0.000005    0.051926    0.009982    0.000000
 0.6600    0.000001    0.000005    0.051988   -0.003854    0.000000
 0.6800    0.000001    0.000004    0.051769   -0.018123    0.000000
 0.7000    0.000001    0.000004    0.051261   -0.032775    0.000000
 0.7200    0.000001    0.000003    0.050456   -0.047765    0.000000
 0.7400    0.000001    0.000003    0.049348   -0.063049    0.000000
 0.7600    0.000001    0.000002    0.047933   -0.078592    0.000000
 0.7800    0.000001    0.000001    0.046205   -0.094380    0.000000
 0.8000    0.000001    0.000001    0.044161   -0.110450    0.000000
 0.8200    0.000001    0.000000    0.041799   -0.126957    0.000000
 0.8400    0.000001   -0.000001    0.039116   -0.144320    0.000000
 0.8600    0.000001   -0.000002    0.036110   -0.163482    0.000000
 0.8800    0.000001   -0.000002    0.032779   -0.186290    0.000000
 0.9000    0.000001   -0.000003    0.029123   -0.215658    0.000000
 0.9200    0.000001   -0.000004    0.025146   -0.254313    0.000000
 0.9400    0.000001   -0.000005    0.020862   -0.299455    0.000000
 0.9600    0.000001   -0.000006    0.016303   -0.331759    0.000000
 0.9800    0.000001   -0.000007    0.011479   -0.313998    0.000000
 1.0000    0.000001   -0.000008    0.006162   -0.268666    0.000000


 -------- Mode No.  12  (freq = 0.211260E+01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000389   -0.000449   -0.000212   -0.000245    0.000000
 0.0200   -0.000344    0.004871   -0.000187    0.002650    0.000002
 0.0400   -0.000198    0.009655   -0.000108    0.005253    0.000004
 0.0600    0.000039    0.013904    0.000021    0.007564    0.000006
 0.0800    0.000355    0.017615    0.000193    0.009583    0.000008
 0.1000    0.000740    0.020791    0.000402    0.011310    0.000010
 0.1200    0.001183    0.023434    0.000643    0.012748    0.000012
 0.1400    0.001673    0.025548    0.000910    0.013898    0.000014
 0.1600    0.002201    0.027143    0.001197    0.014764    0.000016
 0.1800    0.002756    0.028226    0.001499    0.015354    0.000018
 0.2000    0.003327    0.028813    0.001810    0.015672    0.000020
 0.2200    0.003905    0.028918    0.002124    0.015728    0.000022
 0.2400    0.004481    0.028560    0.002437    0.015533    0.000023
 0.2600    0.005045    0.027762    0.002744    0.015098    0.000025
 0.2800    0.005588    0.026548    0.003040    0.014437    0.000027
 0.3000    0.006104    0.024946    0.003320    0.013565    0.000029
 0.3200    0.006584    0.022987    0.003581    0.012498    0.000031
 0.3400    0.007021    0.020704    0.003819    0.011255    0.000033
 0.3600    0.007410    0.018133    0.004030    0.009855    0.000035
 0.3800    0.007745    0.015311    0.004212    0.008318    0.000037
 0.4000    0.008021    0.012277    0.004362    0.006667    0.000039
 0.4200    0.008235    0.009075    0.004478    0.004923    0.000041
 0.4400    0.008383    0.005745    0.004558    0.003110    0.000043
 0.4600    0.008464    0.002331    0.004602    0.001251    0.000045
 0.4800    0.008476   -0.001122    0.004608   -0.000629    0.000047
 0.5000    0.008419   -0.004571    0.004577   -0.002507    0.000049
 0.5200    0.008294   -0.007970    0.004508   -0.004359    0.000051
 0.5400    0.008101   -0.011277    0.004403   -0.006160    0.000053
 0.5600    0.007843   -0.014448    0.004262   -0.007888    0.000055
 0.5800    0.007524   -0.017442    0.004088   -0.009520    0.000057
 0.6000    0.007147   -0.020218    0.003882   -0.011033    0.000059
 0.6200    0.006717   -0.022738    0.003648   -0.012408    0.000061
 0.6400    0.006240   -0.024966    0.003387   -0.013624    0.000063
 0.6600    0.005721   -0.026868    0.003104   -0.014666    0.000065
 0.6800    0.005167   -0.028412    0.002802   -0.015519    0.000067
 0.7000    0.004587   -0.029570    0.002485   -0.016178    0.000069
 0.7200    0.003987   -0.030317    0.002158   -0.016656    0.000071
 0.7400    0.003377   -0.030630    0.001824   -0.017017    0.000073
 0.7600    0.002765   -0.030489    0.001489   -0.017444    0.000074
 0.7800    0.002161   -0.029880    0.001157   -0.018419    0.000076
 0.8000    0.001573   -0.028788    0.000832   -0.021123    0.000078
 0.8200    0.001012   -0.027204    0.000516   -0.028256    0.000080
 0.8400    0.000488   -0.025121    0.000210   -0.045490    0.000082
 0.8600    0.000011   -0.022536   -0.000090   -0.083318    0.000084
 0.8800   -0.000410   -0.019446   -0.000380   -0.157127    0.000086
 0.9000   -0.000764   -0.015854   -0.000638   -0.278495    0.000088
 0.9200   -0.001041   -0.011762   -0.000781   -0.424902    0.000090
 0.9400   -0.001231   -0.007175   -0.000672   -0.492099    0.000092
 0.9600   -0.001324   -0.002098   -0.000404   -0.339194    0.000094
 0.9800   -0.001312    0.003460   -0.000518   -0.088941    0.000096
 1.0000   -0.001183    0.009495   -0.000679    0.004867    0.000098


 -------- Mode No.  13  (freq = 0.224705E+01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000    0.000000    0.000000    0.002363    0.002727    0.000000
 0.0200    0.000000    0.000000    0.002056   -0.032848    0.000000
 0.0400    0.000000    0.000000    0.001074   -0.064716    0.000000
 0.0600    0.000000    0.000000   -0.000508   -0.092866    0.000000
 0.0800    0.000000    0.000000   -0.002616   -0.117297    0.000000
 0.1000    0.000000   -0.000001   -0.005175   -0.138019    0.000000
 0.1200    0.000000   -0.000001   -0.008112   -0.155054    0.000000
 0.1400    0.000000   -0.000001   -0.011353   -0.168441    0.000000
 0.1600    0.000000   -0.000001   -0.014826   -0.178239    0.000000
 0.1800    0.000000   -0.000001   -0.018459   -0.184525    0.000000
 0.2000    0.000000   -0.000001   -0.022184   -0.187397    0.000000
 0.2200    0.000000   -0.000001   -0.025933   -0.186976    0.000000
 0.2400    0.000000   -0.000001   -0.029642   -0.183404    0.000000
 0.2600    0.000000   -0.000001   -0.033250   -0.176846    0.000000
 0.2800    0.000000   -0.000001   -0.036697   -0.167488    0.000000
 0.3000    0.000000   -0.000001   -0.039932   -0.155538    0.000000
 0.3200    0.000000   -0.000001   -0.042903   -0.141221    0.000000
 0.3400    0.000000   -0.000001   -0.045566   -0.124783    0.000000
 0.3600    0.000000   -0.000001   -0.047882   -0.106487    0.000000
 0.3800    0.000000   -0.000001   -0.049815   -0.086609    0.000000
 0.4000    0.000000   -0.000001   -0.051338   -0.065438    0.000000
 0.4200    0.000000    0.000000   -0.052426   -0.043273    0.000000
 0.4400    0.000000    0.000000   -0.053064   -0.020423    0.000000
 0.4600    0.000000    0.000000   -0.053241    0.002801    0.000000
 0.4800    0.000000    0.000000   -0.052952    0.026084    0.000000
 0.5000    0.000000    0.000000   -0.052199    0.049111    0.000000
 0.5200    0.000000    0.000000   -0.050991    0.071572    0.000000
 0.5400    0.000000    0.000000   -0.049342    0.093160    0.000000
 0.5600    0.000000    0.000000   -0.047272    0.113578    0.000000
 0.5800    0.000000    0.000000   -0.044809    0.132541    0.000000
 0.6000    0.000000    0.000001   -0.041982    0.149776    0.000000
 0.6200    0.000000    0.000001   -0.038831    0.165025    0.000000
 0.6400    0.000000    0.000001   -0.035396    0.178050    0.000000
 0.6600    0.000000    0.000001   -0.031725    0.188630    0.000000
 0.6800    0.000000    0.000001   -0.027869    0.196568    0.000000
 0.7000    0.000000    0.000001   -0.023881    0.201686    0.000000
 0.7200    0.000000    0.000001   -0.019821    0.203831    0.000000
 0.7400    0.000000    0.000001   -0.015749    0.202874    0.000000
 0.7600    0.000000    0.000001   -0.011727    0.198710    0.000000
 0.7800    0.000000    0.000001   -0.007822    0.191257    0.000000
 0.8000    0.000000    0.000001   -0.004099    0.180459    0.000000
 0.8200    0.000000    0.000001   -0.000626    0.166280    0.000000
 0.8400    0.000000    0.000001    0.002529    0.148710    0.000000
 0.8600    0.000000    0.000001    0.005299    0.127761    0.000000
 0.8800    0.000000    0.000001    0.007616    0.103466    0.000000
 0.9000    0.000000    0.000001    0.009412    0.075881    0.000000
 0.9200    0.000000    0.000000    0.010623    0.045071    0.000000
 0.9400    0.000000    0.000000    0.011183    0.011076    0.000000
 0.9600    0.000000    0.000000    0.011027   -0.026154    0.000000
 0.9800    0.000000    0.000000    0.010093   -0.066756    0.000000
 1.0000    0.000000    0.000000    0.008323   -0.110533    0.000000


 -------- Mode No.  14  (freq = 0.527331E+01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000330   -0.000378    0.000025    0.000029    0.000000
 0.0200   -0.000150    0.017867    0.000011   -0.001369    0.000002
 0.0400    0.000364    0.033016   -0.000028   -0.002529    0.000004
 0.0600    0.001150    0.045073   -0.000088   -0.003452    0.000006
 0.0800    0.002146    0.054062   -0.000164   -0.004141    0.000007
 0.1000    0.003292    0.060038   -0.000252   -0.004599    0.000009
 0.1200    0.004528    0.063089   -0.000347   -0.004832    0.000011
 0.1400    0.005797    0.063342   -0.000444   -0.004852    0.000013
 0.1600    0.007045    0.060967   -0.000540   -0.004670    0.000015
 0.1800    0.008220    0.056171   -0.000630   -0.004302    0.000017
 0.2000    0.009277    0.049205   -0.000711   -0.003769    0.000019
 0.2200    0.010175    0.040353   -0.000779   -0.003091    0.000020
 0.2400    0.010881    0.029933   -0.000833   -0.002293    0.000022
 0.2600    0.011365    0.018288   -0.000870   -0.001401    0.000024
 0.2800    0.011606    0.005781   -0.000889   -0.000443    0.000026
 0.3000    0.011593   -0.007213   -0.000888    0.000552    0.000028
 0.3200    0.011317   -0.020317   -0.000867    0.001556    0.000030
 0.3400    0.010782   -0.033157   -0.000826    0.002539    0.000032
 0.3600    0.009995   -0.045371   -0.000766    0.003475    0.000033
 0.3800    0.008973   -0.056623   -0.000687    0.004336    0.000035
 0.4000    0.007739   -0.066601   -0.000593    0.005100    0.000037
 0.4200    0.006319   -0.075034   -0.000484    0.005746    0.000039
 0.4400    0.004749   -0.081692   -0.000364    0.006256    0.000041
 0.4600    0.003065   -0.086396   -0.000235    0.006616    0.000043
 0.4800    0.001307   -0.089016   -0.000100    0.006817    0.000045
 0.5000   -0.000481   -0.089483    0.000037    0.006852    0.000046
 0.5200   -0.002258   -0.087783    0.000173    0.006722    0.000048
 0.5400   -0.003979   -0.083960    0.000304    0.006428    0.000050
 0.5600   -0.005603   -0.078116    0.000429    0.005980    0.000052
 0.5800   -0.007091   -0.070407    0.000543    0.005389    0.000054
 0.6000   -0.008408   -0.061041    0.000644    0.004671    0.000056
 0.6200   -0.009523   -0.050269    0.000729    0.003846    0.000057
 0.6400   -0.010411   -0.038385    0.000797    0.002934    0.000059
 0.6600   -0.011053   -0.025714    0.000846    0.001960    0.000061
 0.6800   -0.011437   -0.012605    0.000875    0.000947    0.000063
 0.7000   -0.011557    0.000574    0.000884   -0.000086    0.000065
 0.7200   -0.011416    0.013450    0.000873   -0.001137    0.000067
 0.7400   -0.011024    0.025646    0.000843   -0.002246    0.000069
 0.7600   -0.010397    0.036798    0.000794   -0.003570    0.000070
 0.7800   -0.009561    0.046555    0.000728   -0.005542    0.000072
 0.8000   -0.008546    0.054593    0.000646   -0.009254    0.000074
 0.8200   -0.007391    0.060617    0.000549   -0.017225    0.000076
 0.8400   -0.006137    0.064365    0.000434   -0.034766    0.000078
 0.8600   -0.004833    0.065618    0.000299   -0.071699    0.000080
 0.8800   -0.003530    0.064197    0.000143   -0.142405    0.000082
 0.9000   -0.002284    0.059966   -0.000012   -0.257568    0.000083
 0.9200   -0.001151    0.052829   -0.000088   -0.395636    0.000085
 0.9400   -0.000190    0.042730    0.000041   -0.458228    0.000087
 0.9600    0.000539    0.029649    0.000286   -0.313745    0.000089
 0.9800    0.000976    0.013590    0.000133   -0.081548    0.000091
 1.0000    0.001063   -0.005422   -0.000082    0.000243    0.000093


 -------- Mode No.  15  (freq = 0.533442E+01 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000    0.000000    0.000000    0.000851    0.000974    0.000000
 0.0200    0.000000    0.000000    0.000378   -0.046880    0.000000
 0.0400    0.000000   -0.000001   -0.000970   -0.086561    0.000000
 0.0600    0.000000   -0.000001   -0.003030   -0.118081    0.000000
 0.0800    0.000000   -0.000001   -0.005639   -0.141507    0.000000
 0.1000    0.000000   -0.000001   -0.008637   -0.156981    0.000000
 0.1200    0.000000   -0.000001   -0.011867   -0.164744    0.000000
 0.1400    0.000000   -0.000001   -0.015178   -0.165137    0.000000
 0.1600    0.000000   -0.000001   -0.018426   -0.158611    0.000000
 0.1800    0.000000   -0.000001   -0.021480   -0.145727    0.000000
 0.2000    0.000000   -0.000001   -0.024217   -0.127151    0.000000
 0.2200    0.000000   -0.000001   -0.026533   -0.103645    0.000000
 0.2400    0.000000   -0.000001   -0.028336   -0.076057    0.000000
 0.2600    0.000000    0.000000   -0.029554   -0.045303    0.000000
 0.2800    0.000000    0.000000   -0.030133   -0.012347    0.000000
 0.3000    0.000000    0.000000   -0.030040    0.021814    0.000000
 0.3200    0.000000    0.000000   -0.029259    0.056175    0.000000
 0.3400    0.000000    0.000001   -0.027798    0.089748    0.000000
 0.3600    0.000000    0.000001   -0.025681    0.121580    0.000000
 0.3800    0.000000    0.000001   -0.022952    0.150778    0.000000
 0.4000    0.000000    0.000001   -0.019673    0.176532    0.000000
 0.4200    0.000000    0.000002   -0.015919    0.198129    0.000000
 0.4400    0.000000    0.000002   -0.011779    0.214977    0.000000
 0.4600    0.000000    0.000002   -0.007355    0.226612    0.000000
 0.4800    0.000000    0.000002   -0.002752    0.232715    0.000000
 0.5000    0.000000    0.000002    0.001916    0.233119    0.000000
 0.5200    0.000000    0.000002    0.006535    0.227808    0.000000
 0.5400    0.000000    0.000002    0.010991    0.216923    0.000000
 0.5600    0.000000    0.000002    0.015176    0.200758    0.000000
 0.5800    0.000000    0.000002    0.018989    0.179750    0.000000
 0.6000    0.000000    0.000001    0.022338    0.154467    0.000000
 0.6200    0.000000    0.000001    0.025144    0.125599    0.000000
 0.6400    0.000000    0.000001    0.027343    0.093940    0.000000
 0.6600    0.000000    0.000001    0.028889    0.060365    0.000000
 0.6800    0.000000    0.000000    0.029751    0.025812    0.000000
 0.7000    0.000000    0.000000    0.029921   -0.008740    0.000000
 0.7200    0.000000    0.000000    0.029408   -0.042296    0.000000
 0.7400    0.000000   -0.000001    0.028243   -0.073865    0.000000
 0.7600    0.000000   -0.000001    0.026473   -0.102486    0.000000
 0.7800    0.000000   -0.000001    0.024169   -0.127244    0.000000
 0.8000    0.000000   -0.000001    0.021415   -0.147295    0.000000
 0.8200    0.000000   -0.000001    0.018313   -0.161877    0.000000
 0.8400    0.000000   -0.000001    0.014981   -0.170326    0.000000
 0.8600    0.000000   -0.000002    0.011545   -0.172081    0.000000
 0.8800    0.000000   -0.000001    0.008144   -0.166692    0.000000
 0.9000    0.000000   -0.000001    0.004925   -0.153820    0.000000
 0.9200    0.000000   -0.000001    0.002038   -0.133236    0.000000
 0.9400    0.000000   -0.000001   -0.000361   -0.104840    0.000000
 0.9600    0.000000   -0.000001   -0.002116   -0.068680    0.000000
 0.9800    0.000000    0.000000   -0.003071   -0.024933    0.000000
 1.0000    0.000000    0.000000   -0.003071    0.026408    0.000000


 -------- Mode No.  16  (freq = 0.101362E+02 Hz)

span_loc   s-s disp   s-s slope   f-a disp   f-a slope   twist

 0.0000   -0.000183   -0.000208   -0.000013   -0.000015    0.000000
 0.0200    0.000092    0.026630    0.000007    0.001918   -0.000002
 0.0400    0.000839    0.046899    0.000060    0.003378   -0.000004
 0.0600    0.001925    0.060653    0.000139    0.004369   -0.000006
 0.0800    0.003222    0.068060    0.000232    0.004902   -0.000007
 0.1000    0.004607    0.069429    0.000332    0.005001   -0.000009
 0.1200    0.005962    0.065232    0.000429    0.004698   -0.000011
 0.1400    0.007183    0.056107    0.000517    0.004041   -0.000013
 0.1600    0.008179    0.042845    0.000589    0.003086   -0.000015
 0.1800    0.008876    0.026371    0.000639    0.001899   -0.000017
 0.2000    0.009219    0.007714    0.000664    0.000556   -0.000018
 0.2200    0.009177   -0.012037    0.000661   -0.000867   -0.000020
 0.2400    0.008738   -0.031773    0.000629   -0.002288   -0.000022
 0.2600    0.007913   -0.050414    0.000570   -0.003631   -0.000024
 0.2800    0.006735   -0.066958    0.000485   -0.004823   -0.000026
 0.3000    0.005255   -0.080521    0.000379   -0.005800   -0.000028
 0.3200    0.003539   -0.090382    0.000255   -0.006510   -0.000029
 0.3400    0.001668   -0.096010    0.000120   -0.006915   -0.000031
 0.3600   -0.000271   -0.097092   -0.000019   -0.006993   -0.000033
 0.3800   -0.002185   -0.093543   -0.000157   -0.006737   -0.000035
 0.4000   -0.003983   -0.085512   -0.000287   -0.006159   -0.000037
 0.4200   -0.005578   -0.073370   -0.000402   -0.005284   -0.000039
 0.4400   -0.006894   -0.057693   -0.000497   -0.004155   -0.000040
 0.4600   -0.007867   -0.039233   -0.000567   -0.002826   -0.000042
 0.4800   -0.008450   -0.018878   -0.000609   -0.001360   -0.000044
 0.5000   -0.008616    0.002388   -0.000621    0.000172   -0.000046
 0.5200   -0.008356    0.023536   -0.000602    0.001696   -0.000048
 0.5400   -0.007682    0.043545   -0.000553    0.003137   -0.000050
 0.5600   -0.006628    0.061447   -0.000477    0.004426   -0.000051
 0.5800   -0.005244    0.076381   -0.000378    0.005502   -0.000053
 0.6000   -0.003597    0.087632   -0.000259    0.006313   -0.000055
 0.6200   -0.001767    0.094666   -0.000127    0.006820   -0.000057
 0.6400    0.000159    0.097160    0.000012    0.007001   -0.000059
 0.6600    0.002088    0.095018    0.000151    0.006849   -0.000061
 0.6800    0.003930    0.088375    0.000283    0.006379   -0.000062
 0.7000    0.005596    0.077594    0.000403    0.005625   -0.000064
 0.7200    0.007010    0.063248    0.000505    0.004655   -0.000066
 0.7400    0.008107    0.046098    0.000585    0.003592   -0.000068
 0.7600    0.008841    0.027053    0.000638    0.002684   -0.000070
 0.7800    0.009183    0.007135    0.000664    0.002460   -0.000072
 0.8000    0.009128   -0.012571    0.000664    0.004104   -0.000074
 0.8200    0.008689   -0.030959    0.000641    0.010208   -0.000075
 0.8400    0.007905   -0.046959    0.000603    0.026124   -0.000077
 0.8600    0.006834   -0.059568    0.000561    0.061654   -0.000079
 0.8800    0.005551   -0.067900    0.000523    0.131085   -0.000081
 0.9000    0.004151   -0.071209    0.000481    0.245006   -0.000083
 0.9200    0.002740   -0.068909    0.000368    0.382050   -0.000085
 0.9400    0.001435   -0.060585    0.000072    0.444817   -0.000086
 0.9600    0.000359   -0.045987   -0.000302    0.303332   -0.000088
 0.9800   -0.000362   -0.025005   -0.000234    0.076677   -0.000090
 1.0000   -0.000599    0.002360   -0.000047    0.000332   -0.000092

.
.
.
=================================================================================


When copying the results as above into the respective x- and y- columns into the ModeShapePolyFitting.xls the results seem a bit odd to us. We would expect results which allow a more clear distinction between FA and SS Modeshapes.
But when having a look on the results from BModes distinguishing between FA and SS modeshapes is not easy. I have attached the plots generated from ModeShapePolyFitting.xls for the first 16 frequencies. It seems that for Freq 1-11 it is clear that those are for FA. For the 12th freq it seams a little unclear. 13 and 15 seem to be FA while 14 and 16 perhaps SS shapes.

I have very little experience with this. From what I learned from Paul, it should be clearly visible for each frequency if it is a FA or SS freq. So I would like to ask you for your opinion. Do the results look reasonable to you? Do you have an idea which mistake I could have made?

I have uploaded the plots to our fileshare:
https://unibox.uni-rostock.de/getlink/f ... jQrNoFC6h/

Thank you,
Daniel

Jason.Jonkman
Posts: 4224
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

Postby Jason.Jonkman » Thu Jul 04, 2019 9:37 pm

Dear Daniel,

A few comments/questions:
  • Are the frequencies output by BModes what you'd expect them to be? If not, this could point to a possible bug in the input file settings.
  • I see that you have the (4,4) and (5,5) elements of the hydrostatic stiffness matrix (hydro_K) as negative-valued. This makes sense for the FAST / HydroDyn input, because gravitational restoring is intrinsically accounted for in the ElastoDyn module. But gravitational restoring is not intrinsically accounted for in BModes, so, I would guess hydro_K (4,4) and (5,5) should be positive-valued in BModes (perhaps this is a bug in your BModes input?).
  • BModes does not distinguish between tower modes and platform modes. For a floating turbine, often the first six modes are rigid-body modes of the platform at low frequency, perhaps with a bit of coupling to tower deflections. The heave mode is often difficult to spot from the BModes output file because the tower axial displacement is not output in this file. Regardless, in this case, the tower modes would not start until mode 7.
  • Often the first tower fore-aft and side-to-side modes have quite similar frequency. Likewise for the second tower fore-aft and side-to-side modes, etc.
  • Not including the six rigid-body modes of the platform, I would expect the first tower fore-aft and side-to-side modes to have a slope that doesn't change sign, and the second tower fore-aft and side-to-side modes to have a slope that changes sign once, etc.
  • Assuming your floating wind turbine is symmetric about the XZ plane, I would expect the tower fore-aft modes to be uncoupled from tower torsion (twist), whereas the side-to-side modes would be coupled to tower torsion because of the offset of the rotor mass from the tower centerline.
  • When calculating the mode shape for use in FAST / ElastoDyn, I suggest setting the slope at bottom (dy/dx) to equal the slope at span_loc = 0.0.
I hope that helps.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Daniel.Walia
Posts: 19
Joined: Thu Dec 15, 2016 7:56 am
Organization: University of Rostock
Location: Germany

Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

Postby Daniel.Walia » Thu Jul 25, 2019 4:33 am

Dear Jason,

thank you. It took me a while to come back to your suggestions and answers, as I had some problems to acess the results from our decay tests in the wave tank, in order to answer your questions. And also to dig deeper and understand the relations between the different matrices and their meanings for HydroDyn/BModes/AQWA/WAMIT. Because it got me confused again. Even though you have it explained quite often in this forum.

Jason.Jonkman wrote:
  • Are the frequencies output by BModes what you'd expect them to be? If not, this could point to a possible bug in the input file settings.


When having our 1:50 physical model tested, we have carried out also dedicated decay tests to find out the natural frequencies of the substructure. However, from my understanding the test setup was not suitable to account for the natural frequencies of the tower. We have used an optical motion tracking system and attached reflective bulbs to the substructure. Therefore, only the motions of the substructure have been tracked. Unfortunately we did not monitor the tower or RNA motions themselves. I think this setup does not provide sufficient information to process the towers natural frequency, as the resolution of the optical tracking system is not high enough to track the low amplitude, higher frequency mode shapes of the tower which might be also hidden in the motions of the substructure.
However, the natural frequency of the substructure was found to be at about ~0.021 to 0.025 Hz for Surge as well as for Sway (for the full scale floater as simulated in BModes/FAST).


Jason.Jonkman wrote:
  • I see that you have the (4,4) and (5,5) elements of the hydrostatic stiffness matrix (hydro_K) as negative-valued. This makes sense for the FAST / HydroDyn input, because gravitational restoring is intrinsically accounted for in the ElastoDyn module. But gravitational restoring is not intrinsically accounted for in BModes, so, I would guess hydro_K (4,4) and (5,5) should be positive-valued in BModes (perhaps this is a bug in your BModes input?).


  • Here is where I got confused a little. In the second post of this thread you wrote, that I should augment the (4,4) and (5,5) values of the hydrostatic stiffness matrix with the body weight-related restoring. You have repeated that in your last post and also in other threads. However, in the second post of the thread viewtopic.php?f=4&t=742&hilit=BModes+%3A+Input+parameters+about+tower+support+subsystem#p2824
    you wrote that of the OC3Hywind.bmi you have augmented the mooring_K matrix with the contributions from the body weight-related restoring instead of the hydro_K matrix. So in my matrices above I have added body weight to the (4,4) and (5,5) of the mooring_K matrix instead of the hydro_K matrix. Is the implementation for the HywindOC3 something special? Generally spoken, the correct approach is to add the augmentation to the hydro_K matrix, not to the mooring_K.
    Is this correct?

    The augmentation I for the body weight-related restoring is quite small for our TLP. You have explained it before that the importance is high for deep drafted floaters such as a spar. In our case, the augmentation for our TLP is quite small and equals -m*g*z = -25.05e+06 because our Center of Gravity is located near water level. Therefore, the possible errors in the matrices above will have minor imfluence on our results. Nevertheless, of course it is important to understand where the augmentation should be included correctly.


    Jason.Jonkman wrote:
  • BModes does not distinguish between tower modes and platform modes. For a floating turbine, often the first six modes are rigid-body modes of the platform at low frequency, perhaps with a bit of coupling to tower deflections. The heave mode is often difficult to spot from the BModes output file because the tower axial displacement is not output in this file. Regardless, in this case, the tower modes would not start until mode 7.
  • Often the first tower fore-aft and side-to-side modes have quite similar frequency. Likewise for the second tower fore-aft and side-to-side modes, etc.
  • Not including the six rigid-body modes of the platform, I would expect the first tower fore-aft and side-to-side modes to have a slope that doesn't change sign, and the second tower fore-aft and side-to-side modes to have a slope that changes sign once, etc.
  • Assuming your floating wind turbine is symmetric about the XZ plane, I would expect the tower fore-aft modes to be uncoupled from tower torsion (twist), whereas the side-to-side modes would be coupled to tower torsion because of the offset of the rotor mass from the tower centerline.
  • When calculating the mode shape for use in FAST / ElastoDyn, I suggest setting the slope at bottom (dy/dx) to equal the slope at span_loc = 0.0.
  • .

    I will consider these, when moving on after making sure that I have the correct inputs for BModes. For the moment I will try to meet with the expected natural frequencies for the substructure, to be sure that the implementation of the latter is correct in BModes. When considering the frequencies from the tank tests I think there is at least one more mistake of major influence in the preprocessing of the hydro_K, the hydro_M, or the mooring_K matrix other then the augmentation of the body weight-related restoring.

    Kind Regards,
    Daniel
    Last edited by Daniel.Walia on Tue Jul 30, 2019 7:47 am, edited 1 time in total.

    Jason.Jonkman
    Posts: 4224
    Joined: Thu Nov 03, 2005 4:38 pm
    Location: Boulder, CO
    Contact:

    Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

    Postby Jason.Jonkman » Thu Jul 25, 2019 6:44 am

    Dear Daniel,

    You can include the body weight-related restoring in either the hydro_K or mooring_K matrices in BModes. These matrices are simply summed together internally within BModes anyway.

    Best regards,
    Jason Jonkman, Ph.D.
    Senior Engineer | National Wind Technology Center (NWTC)

    National Renewable Energy Laboratory (NREL)
    15013 Denver West Parkway | Golden, CO 80401
    +1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
    nwtc.nrel.gov

    Daniel.Walia
    Posts: 19
    Joined: Thu Dec 15, 2016 7:56 am
    Organization: University of Rostock
    Location: Germany

    Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

    Postby Daniel.Walia » Fri Jul 26, 2019 1:36 am

    Dear Jason,

    thank you for pointing that out.

    Best regards,
    Daniel

    Daniel.Walia
    Posts: 19
    Joined: Thu Dec 15, 2016 7:56 am
    Organization: University of Rostock
    Location: Germany

    Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

    Postby Daniel.Walia » Thu Aug 29, 2019 8:05 am

    Dear Jason,

    I am still struggling with meeting the expected natural frequencies of our TLP with BModes.
    From the tank tests we got natural frequencies for our symmetric TLP for Surge and Sway at about 0.0215 Hz.
    When running a respective decay test in FAST, with strip theory applied in HD, and MoorDyn used, I meet quite well with the
    above mentioned Surge and Sway frequencies for the TLP. The FAST results are 0.0196 Hz However, I am not able to meet the expected values in BModesJJ.
    Thus, I would like to ask you kindly once again to have a look, in order to rule out possible mistakes in my inputs.

    1. The top of our transition piece, therefore the bottom of our tower is at 30 m above MSL. Thus, draft = - 30 (negatively valued)
    2. The center of mass is 10 m below MSL. Thus, cm_pform = 10 (positively valued)
    3. hub_rad would be 0 for our setup, as there is no "unflexible" part of the tower but the tower is flexible from its very beginning at draft height.
    I obtained the orientation (negatively or positively valued) from your post Tue Nov 06, 2012 6:00 pm viewtopic.php?f=4&t=742&p=2826
    4. I had a mistake before, and therefore I did not use the correctly formated hydro_k and hydro_m matrices. However, by help from Frank Lemmer (from SWE) able to now correctly format the matrices, to meet with the WAMIT definitions as expected by BModes/HydroDyn.

    I have attached the .hst as well as the .1 file.

    Thus, I wrote the hydro_m matrix in the BModes inputs:

    5.858172e+03 0.00000E+00 0.00000E+00 0.00000E+00 -1.075658e+05 0.00000E+00
    0.00000E+00 5.858562e+03 0.00000E+00 1.075658e+05 0.00000E+00 0.00000E+00
    0.00000E+00 0.00000E+00 5.105279e+03 0.00000E+00 0.00000E+00 0.00000E+00
    0.00000E+00 1.074390e+05 0.00000E+00 3.170353e+06 0.00000E+00 0.00000E+00
    -1.074390e+05 0.00000E+00 0.00000E+00 0.00000E+00 3.170353e+06 0.00000E+00
    0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 2.487648e+06

    as well as to the hydro_k matrix:

    0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
    0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
    0.000000e+00 0.000000e+000 2.713241e+01 4.937715e-02 -4.780529e-02 0.000000e+00
    0.000000e+00 0.000000e+00 4.937715e-02 -1.739686e+05 -1.147753e-02 0.000000e+00
    0.000000e+00 0.000000e+00 -4.780529e-02 -1.147753e-02 -1.739686e+05 0.000000e+00
    0.000000e+00 0.000000e+00 0.000000e+00 -1.228136e-02 -2.445528e-03 0.000000e+00

    Herein, (4,4) and (5,5) have to be augmented with the contribution from the body weight-related restoring which I calculated by:

    - m * g * z = -25.05e + 06

    So the new values for (4,4) and (5,5) are: -1.739686e+05 + (-)25.05e + 06 = - 25.223969 *10^6 (negatively valued)

    What is interesting, is that the contribution did not change anything in the resulting frequencies but the 5th or 6th decimal digit in some of the nat. frequencies calculated by BModes.
    Probably this is due to the higher yaw stiffness or/and the shallow draft of the floater.

    5. The mooring stiffness matrix (mooring_k) I received from the standalone python wrapper for MAP++.
    I used the same values for the MAP++ inputs as I have used for MoorDyn, which I use together with my FAST simulation. To keep
    in mind, the results of those FAST simulations do match very well with the tank tests result with regard to the SS/FA substructure
    frequencies. So I think the inputs are plausible. Nevertheless, I tried to play around with the unstretched lengths of the tendons.
    And this - as expected - has a high influence on the floater frequencies.
    So probably something is wrong with my application of MAP++?


    6. The frequencies I got from BModes are

    -------- Mode No. 1 (freq = 0.402640E-01 Hz)
    -------- Mode No. 2 (freq = 0.803631E-01 Hz)
    -------- Mode No. 3 (freq = 0.892912E-01 Hz)
    -------- Mode No. 4 (freq = 0.124583E+00 Hz)
    -------- Mode No. 5 (freq = 0.128184E+00 Hz)
    -------- Mode No. 6 (freq = 0.368710E+00 Hz)
    -------- Mode No. 7 (freq = 0.380267E+00 Hz)
    -------- Mode No. 8 (freq = 0.390270E+00 Hz)
    -------- Mode No. 9 (freq = 0.701860E+00 Hz)
    -------- Mode No. 10 (freq = 0.805302E+00 Hz)
    .
    .
    .

    I would be helpfully for any hint.

    Best regards,
    Daniel
    Attachments
    hst.txt
    (637 Bytes) Downloaded 3 times
    1.txt
    (10.77 KiB) Downloaded 3 times

    Jason.Jonkman
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    Joined: Thu Nov 03, 2005 4:38 pm
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    Contact:

    Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

    Postby Jason.Jonkman » Thu Aug 29, 2019 7:51 pm

    Dear Daniel,

    Your overall approach sounds reasonable. Just a few comments:
    • Your hydro_k and hydro_m matrices seem to match those from your WAMIT output in the attachments. However, the WAMIT output is nondimensional whereas BModes is expecting the data to be dimensional. See the following forum post for information on how to dimensionalize the WAMIT output: viewtopic.php?f=4&t=487&p=1764.
    • For your body weight term, it looks like your z is positive valued i.e. the center of mass is above MSL; is that correct?
    • I would expect the unstretched length of the tendons of a TLP to have a significant effect on the tendon tensions/stiffness and resulting natural frequencies.
    Best regards,
    Jason Jonkman, Ph.D.
    Senior Engineer | National Wind Technology Center (NWTC)

    National Renewable Energy Laboratory (NREL)
    15013 Denver West Parkway | Golden, CO 80401
    +1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
    nwtc.nrel.gov

    Daniel.Walia
    Posts: 19
    Joined: Thu Dec 15, 2016 7:56 am
    Organization: University of Rostock
    Location: Germany

    Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

    Postby Daniel.Walia » Tue Sep 03, 2019 6:02 am

    Dear Jason,
    thank you for your comments.
    Jason.Jonkman wrote:Your hydro_k and hydro_m matrices seem to match those from your WAMIT output in the attachments. However, the WAMIT output is nondimensional whereas BModes is expecting the data to be dimensional. See the following forum post for information on how to dimensionalize the WAMIT output: viewtopic.php?f=4&t=487&p=1764.

    I completely overlooked this. I assumed the inputs for BModes (hydro_m and hydro_k) as of same type as for HydroDyn except the contribution from the body weight-related restoring.
    Jason.Jonkman wrote:For your body weight term, it looks like your z is positive valued i.e. the center of mass is above MSL; is that correct?

    That is correct. You have explained in another thread, that:

    "The augmentation equals -m*g*z, where m is the total system mass (platform + ballast + tower + nacelle + rotor), g is gravity, and z is the vertical location of the center of gravity of the total system mass (z is negative in value for this case)."

    If I take all components (RNA/tower/platform) into account, then the resulting z-position is slightly above MSL. Therefore, z becomes positively valued. Which makes the entire augmentation negatively valued.

    When running BModes with the updated values (dimensional hydro_k and hydro_m matrices for BModes as well the augmentation from body weight-related restoring) I receive the frequencies:

    -------- Mode No. 1 (freq = 0.251306E-01 Hz)
    -------- Mode No. 2 (freq = 0.742124E-01 Hz)
    -------- Mode No. 3 (freq = 0.783866E-01 Hz)
    -------- Mode No. 4 (freq = 0.863897E-01 Hz)
    -------- Mode No. 5 (freq = 0.863897E-01 Hz)
    -------- Mode No. 6 (freq = 0.278128E+00 Hz)

    I also ran BModes without the augmentation and got the following frequencies:

    -------- Mode No. 1 (freq = 0.170019E-01 Hz)
    -------- Mode No. 2 (freq = 0.170019E-01 Hz)
    -------- Mode No. 3 (freq = 0.729952E-01 Hz)
    -------- Mode No. 4 (freq = 0.891731E-01 Hz)
    -------- Mode No. 5 (freq = 0.153203E+00 Hz)
    -------- Mode No. 6 (freq = 0.273859E+00 Hz)

    From the tank tests we know the frequencies should be around 0.0215 for surge and sway.

    At this point I am wondering about the augmentation. You stated at different points that this is necessary due to the influence of the deep draft of the spar and therefore the influence on the pitch-pitch and roll-roll. But we do not have a spar, but a TLP with a much shallower draft. So do you think, the contribution makes sense here? Furthermore, I am asking myself if there is some additional contribution necessary, to account for our floater shape.
    You took the spar shape into account by adding the body weight-related restoring to 4,4 and 5,5 of the matrix. As we have a comparable wide floater with several big buoyancy bodies, probably it makes sense to account for the "semi-sub-like" shape of our structure instead, by adding further contributions to the substructure definition in BModes? However, from my understanding, the hydrodynamic properties (shape of the structure) are well taken into account after including the WAMIT matrices as well as the mooring stiffness matrix. So there is no need to add further augmentations.

    The last thing, where I think I could have a bug in my inputs, is the mooring system. I set up MAP++ standalone using the python wrapper. I defined the MAP++ the same way as I did for MoorDyn which I have coupled to FAST. I directly used the matrix printed by MAP++ as an input for BModes (mooring_k) matrix as shown below. Am I right by directly using the outputs from MAP++ (Linearized stiffness matrix with 0.0 vessel displacement)?

    Code: Select all

     python2 main.py sof_input_nantes.map
    MAP++ (Mooring Analysis Program++) Ver. 1.30.00 Feb-16-2019
    MAP++ environment properties (set externally)...
        Gravity constant          [m/s^2]  : 9.81
        Sea density               [kg/m^3] : 1000.00
        Water depth               [m]      : 200.00
        Vessel reference position [m]      : 0.00 , 0.00 , 0.00

    Linearized stiffness matrix with 0.0 vessel displacement:

    [[ 2.63e+06 -1.61e-10  0.00e+00 -2.47e-09 -8.06e+07  0.00e+00]
     [ 0.00e+00  2.63e+06  0.00e+00  8.06e+07  0.00e+00  0.00e+00]
     [ 2.99e+03  0.00e+00  5.10e+07  0.00e+00 -9.19e+04  0.00e+00]
     [-8.04e-23  8.06e+06 -9.13e-03  1.39e+10 -3.28e-12 -7.05e-11]
     [-8.06e+06  4.94e-10  1.86e-02 -2.74e-01  1.39e+10  3.22e-04]
     [ 2.98e-06  1.31e-06  2.30e-02 -2.49e-01 -2.55e-01  1.26e+08]]

    Linearized stiffness matrix with 5.00 surge vessel displacement:

    [[ 3.29e+05  0.00e+00  1.50e+06  2.24e-04 -1.01e+07 -4.66e-05]
     [ 5.92e-04  2.85e+05  1.99e-02  8.74e+06 -3.63e-01  2.96e-03]
     [ 1.50e+06  0.00e+00  5.09e+07  2.50e-01 -4.59e+07 -7.17e-03]
     [ 6.28e-23  8.06e+06  5.02e-03  1.39e+10  1.23e-01  1.89e-04]
     [-8.06e+06  4.94e-10  5.03e-02  2.42e-01  1.39e+10 -2.89e-04]
     [-1.55e-06 -1.40e-06  1.12e-02  5.05e-01 -7.65e-01  1.26e+08]]
    Line 0: H = 355787.64 [N]  V = 12133601.09 [N]
    Line 0: Fx = 355787.64 [N]  Fy = 0.00 [N]  Fz = 12133601.09 [N]

    These values come from the output buffer as defined in the 'LINE PROPERTIES' portion of the input file
    Labels :  ['T[1]', 'T_a[1]', 'T[2]', 'T_a[2]', 'T[3]', 'T_a[3]']
    Units  :  ['[N]', '[N]', '[N]', '[N]', '[N]', '[N]']
    Values :  ['11198308.26', '11025455.88', '11198308.26', '11025455.88', '11198308.26', '11025455.88']

    Jason.Jonkman
    Posts: 4224
    Joined: Thu Nov 03, 2005 4:38 pm
    Location: Boulder, CO
    Contact:

    Re: Preprocessing Hydrodynamic Properties for BModesJJ / OpenFAST of a floating substructure

    Postby Jason.Jonkman » Tue Sep 03, 2019 11:19 am

    Dear Daniel,

    OK, it sounds like you've now corrected the units of the WAMIT output before using them in BModes.

    I would recommend accounting for the body weight term (-m*g*z) for any floating platform analysis in BModes (spar, semi, TLP). I'm not sure I understand your TLP configuration exactly, but I would expect the BModes approach to be the same for any floating platform.

    Yes, that is the matrix you should be using from MAP++.

    You've stated the natural frequencies you are getting from BModes, but which mode corresponds to the surge and sway natural frequencies? I would expect two modes of similar frequency for both the surge/sway modes and the roll/pitch modes.

    Best regards,
    Jason Jonkman, Ph.D.
    Senior Engineer | National Wind Technology Center (NWTC)

    National Renewable Energy Laboratory (NREL)
    15013 Denver West Parkway | Golden, CO 80401
    +1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
    nwtc.nrel.gov


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