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*Eigenpairs |
 
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*Eigenpairs
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*Eigenpairs |
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To specify the required number of natural frequencies, and also parameters relating to the subspace iteration algorithm.
Refer to Mathematical Background for further information on this feature.
A single line defining the relevant parameters.
No. of Eigenpairs[, Subspace Iteration Convergence
Tolerance] [, Maximum No. of Subspace Iterations] [,
Eigenproblem Shift]
Subspace Iteration Convergence Tolerance defaults to 1x10-6. Maximum No. of Subspace Iterations defaults to 50. Eigenproblem Shift defaults to 1.
Input: |
Description |
No. of Eigenpairs: |
Required number of solution eigenpairs (natural frequencies and mode shapes). See Note (a). |
Subspace Iteration Convergence Tolerance: |
Subspace iteration convergence tolerance. This entry has a default value of 1x10-6. See Notes (b) and (c). |
Maximum No. of Subspace Iterations: |
Maximum number of subspace iterations. This entry defaults to 50 iterations. See Notes (b) and (c). |
Eigenproblem Shift: |
A shift to apply to the eigenproblem. See Note (d). |
(a)When specifying the required number of natural frequencies it is recommended that you specify twice the actual required number you are interested in. For example, if the first 5 natural frequencies are of interest, 10 eigenpairs should be requested. This ensures that the actual required values are estimated to an acceptable accuracy.
(b)Convergence of the subspace iteration procedure is deemed to have been achieved when the normalised change in the eigensolution subspace between successive iterations is less than a specified tolerance. This tolerance is the Subspace Iteration Convergence Tolerance specified here. The Maximum No. of Subspace Iterations input prevents indefinite program looping in non-convergent analyses.
(c)The default values for the convergence measure and maximum number of iterations are sufficient in the vast majority of cases. However, in a small number of cases where the solution is very sensitive, you may need to vary these values.
(d)The basic equation that Modes solves is K v = λ M v, where K and M are stiffness and mass matrices respectively, v is an eigenvector, and λ is the corresponding eigenvalue. Shifting by a value μ means transforming this equation into (K + m M) v = η M v. The eigenvalues of the original and transformed equations are related by ηi = λi + μ for all i eigenvalues. Eigenvectors are identical. Bathe et al., 1976 claim that applying a shift to an eigenproblem can speed convergence and prevent problems when the stiffness matrix is positive semidefinite. By default Modes applies a shift of 1. In a very small number of analyses increasing this value can guarantee convergence which might otherwise not be achieved, but this option should be very rarely used.