3.1.           Normal Modes Analysis

A normal modes analysis of the unreduced model is required as a pre-requisite to many of the other method implemented in TAMKIT. It is performed using Nastran SOL 103 (SEMODES). The analysis may use any of the dynamic reduction and eigensolution methods available in Nastran. The Lanczos method is generally recommended for most problems.

Modal effective mass is one means for selecting critical or target modes of a test arti­cle. The effective mass is a measure of what proportion of the total mass of the test article is being moved by a given mode in a given direction. By definition the sum of modal effective masses across all modes will equal the total mass of the structure[11]. Modal effective mass is requested in Nastran with an MEFFMASS Case Control card. The “FRACSUM” option provides the best presentation of the results for the purpose of selecting target modes[12].

No special processing is required in the normal modes analysis, but a number of the TAM reduction and evaluation methods require the use of the FEM mode shapes. Because of this a Nastran DMAP alter (write_modes) has been provided to write this data in a number of different formats.

A sample input deck for a normal modes analysis is shown in Figure 3-1. Special requirements for the file assignment, executive control, case control, and bulk data portions of the input file are listed below:

·         File Assignment Deck. If the user wants to save the FEM results for later proc­essing, an OUTPUT2 or OUTPUT4 file can be assigned to a FORTRAN unit number. See the ‘OMODES’ parameter in the bulk data section. If the OUTPUT4 option is chosen, this can be written as either an ASCII or a binary file based on the use of a ‘FORMATTED’ or ‘UNFORMATTED’ qualifier on the OUTPUT4 file assignment. ‘UNFORMATTED’ is the default.

·         Executive Control Deck. If the user wants to save the FEM results for later proc­essing, the write_modes alter should 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”).

·         Bulk Data Deck. The bulk data deck must include the standard information for performing a normal modes analysis. If the user wants to save the FEM results for later processing using the write_modes alter, the OMODES parameter should be set as follows:

OMODES < 0            Write the modal frequencies and shapes in OUTPUT2 format to FORTRAN UNIT |OMODES|

OMODES = 0            Write the modal frequencies and shapes to the PCH file in DMI and DMIG format

OMODES > 0            Write the modal frequencies and shapes in OUTPUT4 format to FORTRAN UNIT OMODES

If the write_modes alter is used, selected DOF can be output by placing these in the ‘U2’ set using USET,U2 cards in the bulk data section. If no ‘U2’ set is present all DOF are written.

gpsc_fem.dat

 

ASSIGN OUTPUT4='gpsc_fem.op4' UNIT=13, DELETE

ASSIGN MASTER ='gpsc_fem.MASTER', DELETE

ASSIGN DBALL  ='gpsc_fem.DBALL', DELETE

$

SOL     103     $ Normal modes

$

$  Write modal data

$

INCLUDE 'write_modes.v2001'

$

CEND

TITLE    =GENERAL PURPOSE SPACECRAFT (GPSC)

SUBTITLE =FINITE ELEMENT MODEL (FEM)

$

SPC    = 10             $ Constrain booster interface points

METHOD = 70             $ Modes to 70 Hz

$

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

$

BEGIN BULK

$

PARAM   WTMASS  .00259

PARAM   OMODES  13

$

EIGRL   70      1.0     70.0

$

$  Spacecraft bulk data

$

INCLUDE 'gpsc.blk'

INCLUDE 'gpsc.prp'

$

ENDDATA

Figure 3-1. Sample input file to calculate the FEM normal modes.