Harmonic Perturbation
Analyses in the frequency domain assume that the problem your study is linear, at least with respect to the response to the harmonic excitation. There may be other nonlinearities, such that the structure has responded nonlinearly to a previous loading. This loading could, for example, have caused a large rotations or prestress of a rubber membrane.
The concept of harmonic perturbation is in COMSOL Multiphysics used for distinguishing the linear harmonic analysis from a possible prestress analysis. The most important implication is that if a load has the Harmonic Perturbation selection, it is applied only in a study that is of the perturbation type. A load without this selection is, on the other hand, ignored in such a study. In this way two sets of loads can be distinguished from each other. Technically speaking, the effect of marking a load as Harmonic Perturbation is that the linper() operator is applied to the value of the load.
The default settings for the different structural mechanics study types in the frequency domain are summarized in Table 2-3.
Table 2-3: Default Perturbation Settings for Structural Mechanics Study Types
Study type
study step
Perturbation
Frequency Domain
Frequency Domain
No
Frequency Domain, Prestressed
Stationary
Frequency Domain, Perturbation
No
Yes
Frequency Domain, Modal
Eigenfrequency
Frequency Domain, Modal
N/A
Yes
Frequency Domain, Prestressed, Modal
Stationary
Eigenfrequency
Frequency Domain, Modal
N/A
N/A
Yes
Note the following:
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With the default settings you cannot use the same set of loads for a Frequency Domain and a Frequency Domain, Modal study because only the latter responds to perturbation loads.
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You can change the behavior of a Frequency Domain study to be of the perturbation type by modifying the solver sequence. In the General section of the settings for the Stationary Solver, change Linearity to Linear perturbation.
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A solver that does not have Linearity set to either Linear perturbation or Linear may respond to nonlinear effects. There are multiphysics problems where this is wanted because there may be a nonlinearity in another physics, even though the harmonic solution within structural mechanics is linear. But if there are nonlinearities within the structural mechanics parts of the model, you must be careful with the solver settings.
In a Frequency-Domain, Perturbation study step, that is when Linearity is set to Linear perturbation, geometric nonlinearity will be incorporated in the sense that there is a split between the material and spatial frames. This makes it possible to take for example stiffness from follower loads into account, and to use a contact solution as linearization point.
This frame split was introduced in version 5.3. As an effect, models created in an earlier version, in which some expressions have a frame dependency, may produce results that differ from before. Examples of such cases are:
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Pressure loads
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Loads defined in coordinate systems with deformation dependent axis orientation
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User-defined expressions containing spatial (“lowercase”) coordinates
In the COMSOL Multiphysics Reference Manual:
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Frequency Domain Perturbation Study Step
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Harmonic Perturbation — Exclusive and Contributing Nodes
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Built-In Operators (linper() operator)
For most load types, the use of Harmonic Perturbation is straightforward, but some cases need a more detailed discussion:
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A Rigid Connector can be assigned a Harmonic Perturbation subnode in which you can prescribe harmonic perturbation values to constrained degrees of freedom. If you have added Applied Force or Applied Moment nodes under a Rigid Connector, you can independently assign Harmonic Perturbation to these nodes, so that the loads are considered as being of the perturbation type.
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Even though initial stresses and strains are not usually considered as loads, you can assign Harmonic Perturbation also to the Initial Stress and Strain nodes.
For an example showing how to use harmonic perturbation, see Bracket — Frequency-Response Analysis: Application Library path Structural_Mechanics_Module/Tutorials/bracket_frequency.