Eigen Command

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This command is used to perform the analysis.

analyze <$type> <$solver> $numEigenvalues

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$numEigenvalues	number of eigenvalues required
$type	optional string detailing type of eigen analysis, -standard of -generalized (default generalized)
$solver	optional string detailing type of solver, -UmfPack, -genBandArpack, -symmBandLapack, -SuperLU (default genBandArpack)

RETURNS:

a tcl string containg eigenvalues.

NOTES:

1. The eigenvectors are stored at the nodes and can be printed out using a Node Recorder, the nodeEigenvector command, or the Print command.
2. The current eigensolver is able to solve only for N-1 eigenvalues, where N is the number of interial DOFs. When running into this limitation, the user should add negligible masses to additional unrestrained degrees of freedom.

THEORY:

Standard Problem:

<math> \left (K - \lambda I \right ) \Phi = 0 </math>

Generalized Problem:

<math> \left (K - \lambda M \right ) \Phi = 0 </math>

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EXAMPLE:

set eigenvalues [eigenvalue 10];

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Code Developed by: fmk