3.3.           Evaluating TAM Accuracy

TAMKIT provides an alter called ortho that calculates pseudo- and cross-orthogonality and optionally self- and cross-MAC between a set of FEM and TAM modes. This alter is used in an ASET reduction run (any method is acceptable). Guidelines for its use follow:

·         File Assignment Deck. The FEM modes must be written using the write_modes alter. 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 ortho alter must be included before the CEND card.

·         Case Control Deck. Some output request such as DISP(PLOT)=ALL must be included.

·         Bulk Data Deck. The bulk data deck must include the standard information for performing a normal modes analysis including ASET cards to define the TAM 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

There are three optional parameters.  One controls the calculation of MAC as well as orthogonality and the other controls the normalization of the FEM modes.  They are used as follows.

MAC = ‘NO’    Do not calculate and write MAC matrices (default)

MAC = ‘YES’  Do calculate and write MAC matrices

NORMFEM = ‘NO’     Do not renormalize FEM modes (default)

NORMFEM = ‘YES’    Renormalize FEM modes to unit modal mass

RESFOR = ‘NO’          Do not calculate residual forces (default)

RESFOR = ‘YES’         Calculate residual forces and MRPT stiffness

The ortho alter also has the ability to perform orthogonality checks between test and FEM modes. This is important when comparing the FEM to measured results but is not strictly part of evaluating the TAM. To do this the test mode shapes on the A-set DOF must be included as DMIG matrix PHITEST and the test frequencies as DMI matrix TLAMA in the bulk data file.  See Section 2.6 for a discussion of test/analysis correlation using the ortho alter.

The RESFOR parameter controls the calculation of residual forces and MRPT stiffness matrix perturbations required to match test modes.  This is described in greater detail in Section 3.3.

The output from this alter is written to both the .f06 file and the .pch file. The data written to the .pch file in DMI format includes the FEM and TAM frequencies, the pseudo- and cross-orthogonality matrices, and optionally the self- and cross-MAC matrices. If test modes were included in the bulk data, the test frequencies, test pseudo-orthogonalities and test/FEM cross-orthogonalities are also written. A Matlab function read_tam[16] is provided to read this data into a structure. The syntax of read_tam is:

>> tam = read_tam(‘filename.pch’);

where ‘filename.pch’ is the Nastran punch file with the TAM data written by the alters ortho or ‘residual_kinetic_energy.’ The variable tam is a structure with the following fields:

tam.freqfem      real array of FEM frequencies

tam.freqtam      real array of TAM frequencies

tam.freqtest      real array of test frequencies

tam.portho        Pseudo-orthogonality matrix for FEM modes

tam.xortho        Cross-orthogonality matrix between FEM and TAM modes

tam.tortho         Pseudo-orthogonality matrix for test modes

tam.yortho        Cross-orthogonality matrix between FEM and test modes

tam.pmac          Self-MAC matrix for FEM modes

tam.xmac          Cross-MAC matrix between FEM and TAM modes

This data can be plotted in Matlab or written in a comma-delimited format using rpt_tam. The syntax of rpt_tam is:

>> rpt_tam(tam, ‘file.csv’);

where tam is a TAM structure defined above and ‘file.csv’ is a comma-delimited file that can be read into Excel or any other spreadsheet program. The data written to the file includes a “mode comparison” table that provides a comparison between FEM and TAM frequencies and shapes, and a listing of the orthogonality and MAC matrices labeled by frequency. rpt_tam has an option to include a square root of the sum of the squares (RSS) orthogonality calculation in the mode comparison table which takes the RSS of modes within a user specified percent frequency range of the best matched modes. The syntax of that rpt_tam option is:

>> rpt_tam(tam, ‘file.csv’,0.03);

where 0.03 is the percent frequency range.