Sturm Sequence Check on Computed Eigenvalues - CAESAR II - Help

CAESAR II Users Guide

Language
Русский
Product
CAESAR II
Search by Category
Help
CAESAR II Version
12

(Available for: Spectrum, Modal, and Time History)

Specifies usage of the Sturm sequence calculation as described below. Select Y (for yes) or N (for no). Y is the default value.

In most cases, the eigensolver detects modal frequencies from the lowest to the highest frequency. When there is a strong directional dependency in the system, the modes may converge in the wrong order. This could cause a problem if the eigensolver reaches the cutoff number of modes but has not found the modes with the lowest frequency.

This procedure determines the number of modes that should have been found between the highest and lowest frequencies and compares that against the actual number of modes extracted. If those numbers are different, a warning appears. For example, if 22 natural frequencies are extracted for a system, and if the highest natural frequency is 33.5 Hz, the Sturm sequence checks that there are exactly 22 natural frequencies in the model between zero and 33.5+p Hz, where p is a numerical tolerance found from:

The Sturm sequence check fails where there are two identical frequencies at the last frequency extracted. For example, consider a system with the following natural frequencies:

0.6637

1.2355

1.5988

4.5667

4.5667

If you only ask for the first four natural frequencies, a Sturm sequence failure occurs because there are five frequencies that exist in the range between 0.0 and 4.5667 + p (where p is 0.0041). To correct this problem, you can:

  • Increase the frequency cutoff by the number of frequencies not found. (This number is reported by the Sturm sequence check.)

  • Increase the value of Frequency Cutoff (HZ) by some small amount, if the frequency cutoff terminated the eigensolution. This usually allows the lost modes to fall into the solution frequency range.

  • Fix the subspace size at 10 and rerun the job. Increasing the number of approximation vectors improves the possibility that at least one of them contains some component of the missing modes, allowing the vector to properly converge.