Eigenvalue

) study and study step are used to compute the eigenvalues and eigenmodes of a linear or linearized model in a generic eigenvalue formulation where the eigenvalues are not necessarily frequencies. The Eigenvalue study gives you full control of the eigenvalue formulation, in contrast to the eigenfrequency study that is adapted for specific physics interfaces. The Eigenvalue study is typically used for equation-based modeling.

Selecting an Eigenvalue study gives a solver configuration with an Eigenvalue Solver.


	Mesh Selection, Adaptation and Error Estimates, the Include geometric nonlinearity check box, and Study Extensions are described in Common Study Step Settings. There is also detailed information in the Physics and Variables Selection and Values of Dependent Variables sections.

Study Settings

From the list, select a search method:

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(the default), to specify some search criteria manually. See Manual Eigenvalue Search Settings below.

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, to define an eigenvalue search region in a complex plane. See Manual Eigenvalue Search Settings below and The Eigenvalue Solver Algorithm.

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to find all eigenvalues for a filled matrix. This option is only applicable for small eigenvalue problems.

Manual Eigenvalue Search Settings

By default, the physics interfaces suggest a suitable number of eigenvalues to search for. To specify the number of eigenvalues, select the check box in front of the field to specify the number of eigenvalues you want the solver to return (default: 6).


	In a 3D model, the first six eigenvalues are typically zero and correspond to the rigid-body modes of a 3D geometry. You may therefore need to specify a larger amount of eigenvalues. The largest number of eigenvalues that the solver can compute is equal to the number of unconstrained degrees of freedom minus two.

By default, the physics interfaces suggest a suitable value around which to search for eigenvalues. To specify the value to search for eigenvalues around (shift), select the check box in front of the field; you can then specify a value or expression around which the eigenvalue solver should look for solutions to the eigenvalue equation (default: 0).

Use the list to control how the eigenvalue solver searches for eigenvalues around the specified shift value:

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Select (the default value) to search for eigenvalues that are closest to the shift value when measuring the distance as an absolute value.

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Select to search for eigenvalues with a larger real part than the shift value.

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Select to search for eigenvalues with a smaller real part than the shift value.

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Select to search for eigenvalues with a larger imaginary part than the shift value.

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Select to search for eigenvalues with a smaller imaginary part than the shift value.

Eigenvalue Search Region Settings

Use the field to specify the approximate number of eigenvalues you want the solver to return (default: 20).

In the field, you can specify a maximum number of eigenvalues to limit the eigenvalue solver’s search for additional eigenvalues (default: 200).

The check box is selected by default to increase confidence that the solver finds all eigenvalues in the search region.

Under , you define the size of the search region for eigenvalues as a rectangle in the complex plane by specifying the , , , and in the respective text fields. The search region also works as an interval method if the and are equal; the eigenvalue solver then only considers the real axis and vice versa.


	The eigenvalue solver can in some cases return more than the desired number of eigenvalues (up to twice the desired number). These are eigenvalues that the eigenvalue solver finds without additional computational effort.