Footnotes

 

[1] NX Nastran Version 1.0 is identical to MSC.Nastran V2001. The alters are also provided for MSC.Nastran V2004 and V2005. The NX Nastran 4.1 alters will work properly for all NX Nastran versions from 1.0 through 4.1. For the purpose of this User’s Guide, Nastran refers equally to NX Nastran and MSC.Nastran. It is assumed that the user has a Nastran license that allows him or her to run custom DMAP alters.

[2] While the Matlab functions presented here were tested with Matlab Version 6.5.1, they should run equally well with later versions of Matlab.

[3] In the case of a structure that is excited through enforced motion at its base, the input mode shape coefficients can be the modal participation factors (MPF).

[4] See Section 2.6 for a discussion of comparing test and analysis modes.

[5] There are a number of algorithms that do an excellent job of optimizing sensor location when the goal is to maintain linear independence of the modes as measured by a MAC.

[6] MSC.Nastran V70.5 did not have a GPKE option. In this case the user should use the ‘write_gpke.v705’ alter with and output request such as DISP(PLOT)=ALL. The THRESH qualifier on the GPKE card is replaced with a PARAM,THRESH in bulk data.

[7] For this reason GPKE should always be used with the lumped mass formulation in Nastran. This is the default, with a coupled mass option available using the COUPMASS parameter.

[8] Note that while the matrix MGG is diagonal when using a lumped mass formulation, MAA is not necessarily diagonal. This is because rigid elements (RBE2 and RBE3) and MPC equations can redistribute mass. It is possible, therefore that GPKE on the A-set will not be positive on every DOF, though our experience is that this is rarely an issue.

[9] If the A-set selection resulted in an accurate self-orthogonality matrix, the difference associated with renormalizing the FEM mode shapes is very small.

[10] For a symmetric matrix, the singular value decomposition is identical to the eigenvalue decomposition.  Because the self-orthogonality matrix is small, this is a relatively cheap computation.

[11] Since in practice all modes of the FEM are never calculated, the sum of effective mass will be less than the total mass of the structure.

[12] A common practice in the aerospace industry is to define a primary or target mode as any mode having at least 5% modal effective mass in one of the three translational directions.

[13] Generelazied Dynamic Reduction (GDR) was used in Nastran before the implementation of a robust Lanczos algorithm. At this point, neither MSC nor UGS recommend its use, and it is supported largely for legacy models.

[14] OUTPUT4 files can be either formatted or unformatted. The choice is controlled by the appropriate qualifier on the ASSIGN statement. The default is an unformatted OUTPUT4 file. OUTPUT2 files can also be formatted, but this choice is not recommended since it is difficult to read a formatted OUTPUT2 file.

[15] For this simple example even the IRS TAM generates answers that appear to “exact.”  However, the results for the modal and Hybrid TAMs are exact to as many significant digits as printed by Nastran.

[16] The read_tam function utilizes other Matlab functions that are included in the IMAT toolbox, so the IMAT toolbox folder must be in the Matlab system path.

[17] Pseudo and Cross-Orthogonality are discussed in Section 6 (update) of this user guide.

[18] The IGR method requires that massless DOF be statically reduced from the problem before beginning the iterations. This is a standard procedure in Nastran whenever using one of the transformation-based eigen methods such as GIVENS or HOUSEHOLDER. For models with > ~10,000 DOF the static reduction associated with this process requires a huge amount of memory and disk space and will likely fail on all but the largest computers. The largest IGR problem that ATA has calculated was for a model with 185,808 DOF and a starting ASET size of 6,263 DOF. Reducing this model to 500 DOF required a little over 13 hours of CPU and about a peak of 10 GBytes of scratch space and a 10 GByte database. Problems much larger than that will be impractical.

[19] Since a value of GUFILT<1.0 can result in multiple DOF being eliminated at a given step, the algorithm checks that the remaining DOF are never fewer than NGUYAN. If they are, GUFILT is reset to 1.0, and only one DOF is eliminated per step from that iteration forward.

[20] A situation where this may be desirable is where a good candidate set of size 1,000 or so may be desired for other sensor selection schemes such as effective independence or a genetic algorithm approach.

[21] Since a value of EFFILT<1.0 can result in multiple DOF being eliminated at a given step, the algorithm checks that the remaining DOF are never fewer than NGUYAN. If they are, EFFILT is reset to 1.0, and only one DOF is eliminated per step from that iteration forward.

[22] The MWEI method requires that massless DOF be statically reduced from the problem before beginning the iterations. This is a standard procedure in Nastran whenever using one of the transformation-based eigen methods such as GIVENS or HOUSEHOLDER. For models with > ~10,000 DOF the static reduction associated with this process requires a huge amount of memory and disk space and will likely fail on all but the largest computers.

[23] Since a value of EFFILT<1.0 can result in multiple DOF being eliminated at a given step, the algorithm checks that the remaining DOF are never fewer than NDOF. If they are, EFFILT is reset to 1.0, and only one DOF is eliminated per step from that iteration forward.