RKE is calculated in TAMKIT by using the residual_kinetic_energy alter. This alter normalizes the kinetic energy and outputs it in the same manner as the write_gpke alter. Requirements for the use of this alter are as follows:
· File Assignment Deck. If the FEM modes were stored in either OUTPUT2 or OUTPUT4 format, the corresponding file must be assigned to a FORTRAN Unit Number.
· Executive Control Deck. The residual_kinetic_energy alter must be included before the CEND card.
· Case Control Deck. The case control deck must include standard commands for a normal modes analysis (MPC, SPC, DYNRED, and METHOD selections as needed). The mode shapes must be requested using a DISP output request (such as “DISP(PLOT) = ALL”). A GPKE request is not required.
· Bulk Data Deck. The bulk data deck must include the standard information for performing a normal modes analysis including ASET cards to define the initially selected DOF. If the DMIG option was chosen for the FEM mode shapes, these must be included in the bulk data. Otherwise the OMODES parameter must be set as follows:
OMODES < 0 Read the modal frequencies and shapes in OUTPUT2 format from FORTRAN UNIT |OMODES|
OMODES > 0 Read the modal frequencies and shapes in OUTPUT4 format from FORTRAN UNIT OMODES
Additionally, the output of the RKE can be controlled by the following two parameters:
KENORM = ‘NO’ Directly output RKE data with no normalization
KENORM = ‘YES’ Normalize RKE so that total is 100.0 in each mode (default)
KEFILT Only output RKE values greater than KEFILT (default = 0.0)
ORTHO = ‘NO’ Do not calculate pseudo- and cross-orthogonality (default)
ORTHO = ‘YES’ Calculate pseudo- and cross-orthogonality for initial ASET[17]
An example of an RKE run is illustrated in Figure 3-9. This runs starts with just two triaxial accelerometers at grids 18 and 40 as illustrated in Figure 3-10 and requests output of all DOF with RKE of at least 10.0% in each mode.
gpsc_rke.dat
ASSIGN INPUTT4='gpsc_fem.op4', UNIT=13
ASSIGN MASTER ='gpsc_aset.MASTER', DELETE
ASSIGN DBALL ='gpsc_aset.DBALL', DELETE
$
SOL 103 $
$
INCLUDE 'residual_kinetic_energy.v2001'
$
CEND
TITLE =GENERAL PURPOSE SPACECRAFT (GPSC)
SUBTITLE =RESIDUAL KINETIC ENERGIES
$
SPC = 10 $ Constrain booster interface points
METHOD = 70 $ Modes to 70 Hz
$
DISP(PLOT) = ALL $ Recover displacements
$
BEGIN BULK
$
PARAM WTMASS .00259
PARAM OMODES 13
PARAM ORTHO YES
PARAM KENORM YES
PARAM KEFILT 10.0
$
EIGRL 70 1.0 70.0
$
$ Spacecraft bulk data
$
INCLUDE 'gpsc.blk'
INCLUDE 'gpsc.prp'
$
$ Initial DOF to start selection process
$
INCLUDE 'gpsc_init.aset'
$
ENDDATA
Figure 3-9. Sample input file to calculate residual kinetic energies.
![]() |
Figure 3-10. Initial selection of DOF for RKE approach.
Pseudo-orthogonality of the FEM modes with respect to the reduced mass matrix is written to both the .f06 and .pch files. For this case it is listed in Table 3-11.
Table 3-11. Pseudo-Orthogonality of FEM modes with respect to initial 6 DOF mass matrix.
Cross-orthogonality of the FEM modes with respect to the five modes of the reduced TAM is listed in Table 3-12.
Table 3-12. Cross-Orthogonality of FEM/TAM modes with respect to initial 6 DOF mass matrix.
Further details on pseudo- and cross-orthogonality are presented in Section 2.4, but the results presented here indicate that only FEM modes 3 and 4 are well represented by the initial 6 DOF.
Additional DOF that should improve these results are
listed in the .pch file in DMIG format as the matrix RKEF. The DOF in
the punch file can be written to Nastran ASET cards using Matlab function
pch2aset. Only the nonzero values and, in the case of KEFILT,
only those values greater than KEFILT are shown. The .pch file for this
example, which uses a KEFILT value of 10.0, is illustrated in Figure
3-11.
gpsc_rke.pch
DMIG RKEF 0 9 2 0 17
DMIG* RKEF 1 0
* 50 3 9.976635750D+01
DMIG* RKEF 2 0
* 32 3 9.825740887D+01
DMIG* RKEF 3 0
* 32 3 3.202743388D+01
* 50 3 6.616971163D+01
DMIG* RKEF 4 0
* 47 1 1.240917177D+01
* 50 1 1.333430564D+01
DMIG* RKEF 5 0
* 11 3 1.639908165D+01
* 12 3 1.639629007D+01
* 13 3 1.639908206D+01
* 17 3 1.639629048D+01
DMIG* RKEF 6 0
* 11 3 1.640432577D+01
* 12 3 1.640317542D+01
* 13 3 1.640432535D+01
* 17 3 1.640317500D+01
DMIG* RKEF 7 0
* 11 3 1.241488655D+01
* 12 3 1.208851826D+01
* 13 3 1.241488656D+01
* 17 3 1.208851825D+01
DMIG* RKEF 8 0
* 42 2 1.045422358D+01
* 50 2 1.041700059D+01
DMIG* RKEF 9 0
* 11 3 1.062645325D+01
* 12 3 1.061426266D+01
* 13 3 1.062645286D+01
* 17 3 1.061426227D+01
DMIG* RKEF 10 0
* 11 3 1.622298248D+01
* 12 3 1.601123339D+01
* 13 3 1.622298299D+01
* 17 3 1.601123395D+01
Figure 3-11. Punch file with RKE results above 10% for 1st 10 modes.
Examining the .pch file indicates that the 14 DOF listed in Table 3-13 and illustrated in Figure 3-12 should be added to the ASET to improve the accuracy of the TAM:
Table 3-13. Fourteen additional DOF selected by RKE algorithm.
Grid |
Dir |
Grid |
Dir |
Grid |
Dir |
11 |
3 |
32 |
3 |
42 |
12 |
12 |
3 |
33 |
2 |
47 |
1 |
13 |
3 |
34 |
1 |
50 |
123 |
17 |
3 |
37 |
1 |
|
|
Figure 3-12. 14 DOF added using RKE algorithm.
After adding these 14 DOF to the original 6 DOF, the pseudo-orthogonality matrix is listed in Table 3-14, and the cross-orthogonality matrix in Table 3-15. These results indicate that all modes, with the exception of mode 15, are very well represented by these 20 DOF. The representation of mode 15 could be further improved by examining the RKE for this mode with the 20 DOF set (6 original plus 14 new) and adding one or more DOF to the list in an iterative manner.
Table 3-14. Pseudo-Orthogonality of FEM modes after adding 15 DOF to the original 6 DOF based on RKE.
Table 3-15. Cross-Orthogonality of FEM/TAM modes after adding 15 to the original 6 DOF DOF based on RKE.
If the .pch file is examined directly, the KEFILT parameter should be used to limit the amount of data written. The same two Matlab functions used to read and report GPKE output can also be used for RKE output. These are read_ke and rpt_ke. See Section 4.2 for further details on the use of these functions. For this example the Matlab session is:
» rke=read_ke('gpsc_rke.pch');
» rpt_ke(rke,'gpsc_rke.csv',[],'gpsc_rke.aset')
The ‘gpsc_rke.csv’ file read into Excel is illustrated in Figure 3-13, and the ASET cards written to ‘gpsc_rke.aset’ are listed in Figure 3-14.
Figure 3-13. Comma-delimited RKE output read into Excel.
$ 14 Aset cards written based on Kinetic Energy results
$
ASET 11 3
ASET 12 3
ASET 13 3
ASET 17 3
ASET 32 3
ASET 33 2
ASET 34 1
ASET 37 1
ASET 42 12
ASET 47 1
ASET 50 123