*COMPLEX FREQUENCY

Extract complex eigenvalues and modal vectors.

This option is used to perform eigenvalue extraction to calculate the complex eigenvalues and corresponding complex mode shapes of a system.

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Complex Eigenvalue Extraction

ProductsAbaqus/StandardAbaqus/CAE

TypeHistory data

LevelStep

Abaqus/CAEStep module

Optional parameters

FRICTION DAMPING

Set FRICTION DAMPING=NO (default) to ignore friction-induced damping effects.

Set FRICTION DAMPING=YES to include friction-induced damping effects.

NORMALIZATION

Set NORMALIZATION=DISPLACEMENT (default for SIM-based analyses) to normalize the complex eigenvectors so that the real part of the largest value in each vector is unity and the imaginary part is zero.

Set NORMALIZATION=MODAL (the only option for analyses that are not based on the SIM architecture) to normalize only the complex eigenvectors of the projected system.

PROPERTY EVALUATION

Set this parameter equal to the frequency at which to evaluate frequency-dependent properties for viscoelasticity, springs, and dashpots during complex eigenvalue extraction. If this parameter is omitted, Abaqus/Standard will evaluate the material properties associated with frequency-dependent springs and dashpots at zero frequency and will not consider the contributions from frequency-domain viscoelasticity in the COMPLEX FREQUENCY step.

STIFFNESS PROJECTION

Set STIFFNESS PROJECTION=YES (default) to project the stiffness operator on the modal subspace.

Set STIFFNESS PROJECTION=NO to skip projection of the stiffness operator on the modal subspace. In this case the diagonal matrix of the real eigenvalues corresponding to the modal subspace basis vectors is used as a modal stiffness operator and some advanced mechanical effects (such as friction-induced effects, frequency-dependent properties, and other effects) are ignored. This option can significantly reduce the computational time in the stiffness projection phase of the analysis, but it should be used with caution.

Set STIFFNESS PROJECTION=CONTACT ONLY if advanced mechanical properties (for example, friction) are localized in the contact area only and the rest of the model has the same properties as in the preceding real eigenfrequency extraction analysis. In this case the modal stiffness operator is combined from the diagonal matrix of the real eigenvalues corresponding to the modal subspace basis vectors and the projection of the additional contact stiffness terms on the modal subspace. This option can significantly reduce the computational time in the stiffness projection phase of the analysis, but it should be used with caution.

UNSTABLE MODES ONLY

Set this parameter equal to the cutoff value for complex modes. Only complex modes with the real part of the eigenvalue higher than the cutoff value are processed for output. The default value of this parameter is 0.0. If this parameter is omitted, all complex modes are output.

Optional, mutually exclusive parameters

LEFT EIGENVECTORS

Include this parameter to request left complex eigenvectors. This parameter is relevant only in analyses that are based on the SIM architecture.

RIGHT EIGENVECTORS

Include this parameter (default) to request right complex eigenvectors.

Data line for complex eigenvalue extraction

First (and only) line

  1. Number of complex eigenmodes to be extracted. If this entry is omitted, all the eigenmodes available in the projected subspace, formulated on the basis of all eigenmodes computed in the preceding FREQUENCY step and possibly reduced by using the SELECT EIGENMODES option, will be extracted.

  2. Minimum frequency of interest, in cycles per time. If this field is left blank, no minimum is set.

  3. Maximum frequency of interest, in cycles per time. If this field is left blank, no maximum is set.

  4. Shift point, S, in cycles per time (S ≥ 0). The eigenvalues with the imaginary part closest to this point are extracted. The default value is zero.