SOLVERS Home: Modes

Description

Applicable to the Linear Buckling and Natural Frequency solvers.

Modes

Specifies the number of modes (i.e., eigenvalues) to be calculated.

Shift

Specifies the shift value to be used in the eigenvalue analysis.

The default shift is zero, which means that the smallest buckling factors (by magnitude), and the lowest frequencies, are calculated. Buckling factors can be positive or negative, whereas frequencies are always positive.

If a non-zero shift is used, the buckling load factors or frequencies closest to the shift value, above and below the value, are calculated.

Besides the purpose described above, the shift can also be used to enable the solution of the natural frequencies of an unrestrained structure. With a shift of zero, such a structure will produce a singular stiffness matrix, so the factorisation procedure will fail before the eigenvalue extraction procedure can even start. By setting the shift to a negative value, the matrix will no longer be singular and the lowest modes will be found. The magnitude of a negative shift is typically set to a value an order of magnitude or so smaller than the lowest deformational mode expected in the structure; experimentation is sometimes required.

Sturm Check

If set, a Sturm check is performed after the eigenvalues have been extracted.

The Sturm check is used to ensure that the number of eigenvalues calculated in the reported range is correct. That is, that no modes in the reported range were missed, and that the reported range does not have more modes than it should. The operation cannot verify the eigenvalues, only the number of eigenvalues that should exist in the range.

The sub-space algorithm used for the extraction of eigenvalues in Straus7 involves an iterative numerical procedure, and therefore is not guaranteed to locate all the requested modes. The Sturm check can be used to determine the exact number of eigenvalues within a specified range. This range is set automatically by the solver to cover all the eigenvalues found.