7.4.           EXPAND_MODES Alter

 

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$  Rigid Format 103 - Normal modes analysis

$  MSC/NASTRAN Version 2001

$

$

$     ******************************************************

$     *****            COPYRIGHT  (C)  2003            *****

$     *****          BY ATA ENGINEERING INC.           *****

$     *****             ALL RIGHTS RESERVED            *****

$     ******************************************************

$

$     09-03- ATA/Paul Blelloch

$

$  Description:

$

$  This alter expands test mode shapes using either the standard expansion

$  shapes stored in GOA or optionally dynamic expansion for each mode.  If

$  modal effective mass is requested in Case Control, it will also calculate

$  effective mass of the test modes.

$

$  The test mode shapes must be provided as matrix PHITEST in DMIG format.

$  The test frequencies must be provided as matrix TLAMA in DMI format.

$  The TLAMA matrix has one column for each mode.  The first row is the

$  modal frequency, the second row is 0.0 and the third row is the modal

$  generalized mass.  The mode shapes can optionally be normalized to unit

$  modal mass, in which case this column is ignored.

$

$  By default this alter uses the GOAD matrix to expand all modes at once.  This

$  will usually be a static expansion matrix, though it can be any other

$  expansion matrix through the use of the appropriate alters.  Alternatively

$  the user can perform a mode by mode dynamic expansion.  The expansion

$  shapes in this case are recalculated for each mode as follows:

$

$                     2       -1           2

$  GOAD  = -([KOO] - W *[MOO])  *([KOA] - W [MOA])

$

$  where:

$

$  W     - Frequency (rad/sec) for that test mode

$

$  If the user chooses the dynamic expansion method, he can also calculate

$  residual forces and a minimum rank stiffness matrix perturbation that

$  will match the test data.  These are powerful error localization

$  techniques.  The residual force matrix has a column associated with

$  every test mode and is non-zero only on measured DOF.  It is calculated

$  as follows:

$

$  R = K*PHI - M*PHI*LAMBDA

$

$  where:

$  PHI    - Matrix of test mode shapes

$  LAMBDA - Diagonal matrix of test eigenvalues

$

$  The stiffness matrix perturbation is given by:

$

$           T     -1  T

$  DK = R*(R *PHI)  *R

$

$  The stiffness matrix perturbation is output as DKGG.  It is also normalized

$  on a term by term basis by KAA and output as RKGG, and finally the diagonal

$  elements of RKGG are output as RKGGD.

$

$  Special instructions to use this alter:

$-----------------------------------------------------------------------

$  FILE MANAGEMENT SECTION (FMS)

$

$

$  

$    If the orthogonality option is chosen it required the input of FEM

$    mode shapes.  The format of these is controlled by PARAM,OMODES

$

$    If the OUTPUT2 or OUTPUT4 options are chosen these should be assigned

$

$    ASSIGN INPUTT4=fem_modes.op4 UNIT=11

$

$    or

$

$    ASSIGN INPUTT2=fem_modes.op2 UNIT=11

$

$    Note that a formatted OUTPUT4 file can be used as follows

$

$    ASSIGN INPUTT4=fem_modes.op4 UNIT=11 FORMATTED

$-----------------------------------------------------------------------

$  EXECUTIVE CONTROL DECK

$

$    SOL 103

$    Include this alter immediately before the CEND statement

$

$-----------------------------------------------------------------------

$  CASE CONTROL DECK

$

$    No special input is required.  The Case Control deck must include

$    standard modal solution requests (SPC, METHOD, etc.).  Some output

$    request such as DISP(PLOT)=ALL is required to force data recovery.

$

$-----------------------------------------------------------------------

$  BULK DATA DECK

$

$    Optional parameters:

$

$    PARAM,OMODES,I  <0 : Read FEM modes from OUTPUT2 file UNIT = |OMODES|

$                     0 : Read FEM modes from DMIG cards in bulk data

$                    >0 : Read FEM modes from OUTPUT4 file UNIT = OMODES

$

$    PARAM,ORTHO,CHAR8 'YES' : Calculate TEST/TAM cross-orthogonality

$                      'NO'  : Do not calculate any orthogonality (default)

$

$    PARAM,EXPAND,CHAR8 'DYNAMIC' : Use mode by mode dynamic expansion

$                       'GUYAN'   : Use GOA matrix to expand modes (default)

$                       'SEREP'   : Use SEREP expansion (must have FEM modes)     

$                       'XORTHO'  : Use cross orthogonality expansion (must have FEM modes)     

$                       'TORTHO'  : Use TAM cross orthogonality expansion

$

$    PARAM,TMODORT,CHAR8 'YES' : Orthogonalize Test Modes using Barach's Method

$                        'NO'  : Do not orthogonalize test modes (Default)

$

$    PARAM,RESFOR,CHAR8 'YES' : Calculate residual forces and MRPT stiffness

$                       'NO'  : Do not calculate residual forces (default)

$

$    The residual force calculation only works with dynamic expansion.  It will

$    not produce any results with Guyan, SEREP or cross orthogonality expansion

$

$    Note that FEM mode shapes are only required if PARAM,ORTHO,YES is set or if

$    SEREP or cross-orthogonality expansion are chosen. In these cases

$    test mode shapes must be included on a DMIG matrix named PHITEST.  The

$    test frequencies must be included on a DMI matrix called TLAMA.

$

$-----------------------------------------------------------------------

$  EXAMPLE NASTRAN DECKS

$

$

$    ASSIGN  INPUTT4='gpsc_modes.op4' UNIT=11 OLD

$    ASSIGN  MASTER='gpsc_aset.MASTER'

$    ASSIGN  DBALL ='gpsc_aset.DBALL'

$    RESTART

$    $

$    SOL     103

$    INCLUDE expand_modes.v2001

$    CEND

$    $

$    TITLE    = GENERAL PURPOSE SPACECRAFT

$    SUBTITLE = TEST MODE EXPANSION

$    LABEL    = DYNAMIC EXPANSION

$    $

$    MEFFMASS(ALL) = YES         $ Calculate modal effective mass

$    $

$    SPC = 1

$    METHOD = 50                 $ Modes to 50 Hz

$    $

$    DISP(PLOT) = ALL            $ Recover but don't print displacements

$    $

$    BEGIN BULK

$    $

$    PARAM,ORTHO,YES             $ Calculate orthogonality

$    PARAM,OMODES,11             $ Read FEM shapes from OUTPUT4 Unit 11

$    PARAM,EXPAND,DYNAMIC        $ Use dynamic expansion

$    $

$    ENDDATA

$

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