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