3.2.1.      Creating a Static TAM

A static TAM is the easiest type of TAM to create. A static TAM requires no spe­cial input beyond the generic items described in Section 3.2. The matrix operations used to perform the static (Guyan) reduction are a standard feature of SOL 103 and are activated by the presence of ASET and/or ASET1 cards in the Bulk Data deck.

No special differences are needed for superelement or non-superelement models beyond those listed in Section 1.5.

A sample input file to create a static TAM is shown in Figure 3-2. This includes the ortho alter to calculate pseudo- and cross-orthogonality. This alter is better described in Section 3.3.

gpsc_stam.dat

 

ASSIGN INPUTT4='gpsc_fem.op4', UNIT=13

ASSIGN MASTER ='gpsc_stam.MASTER', DELETE

ASSIGN DBALL  ='gpsc_stam.DBALL',  DELETE

$

SOL     103     $ Normal modes

INCLUDE 'ortho.v2001'

CEND

TITLE    =GENERAL PURPOSE SPACECRAFT (GPSC)

SUBTITLE =TAM - STATIC REDUCTION AND ORTHOGONALITY

$

SPC    = 10             $ Constrain booster interface points

METHOD = 70             $ Modes to 70 Hz

$

DISP(PLOT) = ALL        $ Recover but do not print mode shapes

$

BEGIN BULK

$

$  PARAMeter cards

$  ---------------

$

PARAM   GRDPNT  0

PARAM   USETPRT 0

PARAM   WTMASS  .00259

PARAM     OMODES    13

$

$  Compute eigenvalues using the Lanczos method

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

$

EIGRL   70              70.

$

$  Spacecraft bulk data

$  --------------------

$

INCLUDE 'gpsc.blk'

INCLUDE 'gpsc.prp'

$

$  Static reduction data

$  ---------------------

$

INCLUDE 'gpsc_rke1.aset'

$

ENDDATA

Figure 3-2. No special input requirements are needed to create a Static TAM.

For this example, the pseudo-orthogonality of the FEM mode shapes with respect to the statically reduced mass matrix is presented in Table 3-1. The cross-orthogonality between the TAM and FEM mode shapes is presented in Table 3-2. The interpreta­tion of the pseudo- and cross-orthogonality matrices is further dis­cussed in Section 2.4 but the static TAM does a fairly good job of representing these seventeen modes.

Table 3-1. Pseudo-orthogonality of FEM modes w.r.t. statically reduced mass matrix.

Table 3-2. Cross-orthogonality of TAM/FEM modes w.r.t. statically reduced mass matrix.