Eigenfrequency

) study and study step are used to compute eigenmodes and eigenfrequencies of a linear or linearized model.

For example, in electromagnetics, the eigenfrequencies correspond to the resonant frequencies and the eigenmodes correspond to the normalized electromagnetic field at the eigenfrequencies. In solid mechanics, the eigenfrequencies correspond to the natural frequencies of vibrations and the eigenmodes correspond to the normalized deformed shapes at the eigenfrequencies. In acoustics, the eigenfrequencies correspond to the resonant frequencies and the eigenmodes correspond to the normalized acoustic field at the eigenfrequencies.

Selecting an Eigenfrequency study gives a solver with an Eigenvalue Solver. Use this study to solve an eigenvalue problem for a set of eigenmodes and associated eigenfrequencies. Also see The Relationship Between Study Steps and Solver Configurations.


	The Physics and Variables Selection, Values of Dependent Variables, Mesh Selection, Adaptation and Error Estimates, and Geometric Entity Selection for Adaptation sections and the Include geometric nonlinearity check box 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:

•

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

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, to define an eigenfrequency search region in a complex plane. See Eigenvalue Search Region Settings below.

Manual Eigenfrequency Search Settings

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


	In a 3D model, the first six eigenfrequencies are typically zero and correspond to the rigid-body modes of a 3D geometry. You may therefore need to specify a larger amount of eigenfrequencies. The largest number of eigenfrequencies 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 eigenfrequencies. To specify the value to search for eigenfrequencies around (shift), select the check box in front of the field. You can specify a value (as an eigenfrequency) 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 eigenfrequencies around the shift value specified in the field.

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

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

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

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

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


	When using a search for eigenfrequencies, the nonsymmetric eigenvalue solver is always used, even when the problem to solve is symmetric.

Eigenfrequency Search Region Settings

Use the field to specify the approximate number of eigenfrequencies you want the solver to return (default: 20). The value of the will affect the used by the algorithm; see the section of the Eigenvalue Solver. It means that increasing the value of the will increase the memory requirement and the computational time. If the solver indicates that the value of the is smaller than the actual number of eigenfrequencies in the given region, it will perform a search for more eigenfrequencies, which increases the computational time; see The Eigenvalue Region Algorithm. Within limits it is often more efficient to provide a too large value of than a too small.

In the field, you can specify a maximum number of eigenfrequencies 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 eigenfrequencies in the search region. The work required for performing the consistency check constitutes a significant part of the total work of the eigenfrequency computation.

Under , you define the size of the search region for eigenfrequencies 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 eigenfrequencies (up to twice the desired number). These are eigenfrequencies that the eigenvalue solver finds without additional computational effort.

Symmetry Settings

Eigenvalue computations can be performed with a nonsymmetric solver or, if applicable, a real symmetric solver, which improves performance if applicable. From the list, choose (the default) or . For the option there is the option to select the check box. This check increases the computational time and memory requirements but provides a rigorous check of the applicability of the real symmetric solver.

Study Extensions

This section contains some optional extensions of the study, such as auxiliary sweeps (see Common Study Step Settings). Adding an auxiliary parametric sweep adds an Eigenvalue Parametric attribute node to the Eigenvalue Solver.

Distribute Parametric Solver

If you are running an auxiliary sweep and want to distribute it by sending one parameter value to each compute node, select the check box. To enable this option, click the button (

) and select in the dialog box.


	Tuning Fork: Application Library path COMSOL_Multiphysics/Structural_Mechanics/tuning_fork. For a model that uses a search region for the eigenfrequencies, with the Acoustics Module, see Helmholtz Resonator Analyzed with Different Frequency Domain Solvers: Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/helmholtz_resonator_solvers.