COMSOL 6.2 - Periodic Condition

Periodic Condition

Use a to prescribe that the displacements and rotations in two sets of entities with the same geometrical shape are related as in a periodic structure. In 3D edges can be connected with a periodic condition, and in 2D axisymmetry points. In the Plate interface, the condition can be set up for edges (boundaries).

Several different periodicity types can be prescribed using this boundary condition.

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The , , and periodic conditions directly prescribe relations both between the displacements and between the rotations. They can be used for any study type.

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The can be used for frequency domain problems with a spatial periodicity of the geometry and solution. The modeled structure is typically a unit cell of a repetitive structure.

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The is a special case of a Floquet condition, intended for structures, which consist of a number of sectors that are identical when rotated around a common axis, like in a fan.

The two sets of edges or points between which there is a periodicity condition are called the source and destination. It is not required to have the same mesh on the source and destination, but the local accuracy of the solution near the edges will be better if you use the same mesh.


	For periodic conditions on shells, the periodicity condition acts on edges or points, as opposed to solids and plates where it acts on boundaries. This means that the orientation cannot be determined automatically. You must provide coordinate systems using the Orientation of Source and Orientation of Destination sections. The default coordinate system is the Global coordinate system, which works well if the edges are parallel. In other cases, you need to add a Destination Selection subnode, in order to supply the coordinate system for the destination. In cases of rotational symmetry, you can assign the same cylindrical coordinate system to both source and destination. Note that cylindrical coordinate systems in general cannot be used in situations where they are accessed in points located on the axis of revolution, since axis orientations are not uniquely defined there. Thus, if the edges intersect at the axis of revolution, you must use two different coordinate systems with fixed axis directions, rotated with respect to each other. When there is a common point on the axis of revolution, you should explicitly constrain it to remain on the axis and to have no rotations using Prescribed Displacement/Rotation.

Edge Selection/point Selection/Boundary Selection

Select both the source and destination edges or points.

The software automatically identifies the edges as either source edges or destination edges. This works fine for cases like opposing parallel edges. In more general cases, right-click the Period Condition node and choose Manual Destination Selection to add a section where you can specify the edges which constitute the destination. By default, this node contains the selection that COMSOL Multiphysics has identified.

In cases where the periodic edge is split into several edges within the geometry, it might be necessary to apply separate periodic conditions to each pair of geometric edges for the matching to work properly.


	In the 2D axisymmetry, Edge Selection is replaced by Point Selection. In the Plate interface, Edge Selection is replaced by Boundary Selection.

Destination Selection

This section is available for specifying the destination edges, points, or boundaries, if needed, when the option is selected in the context menu for the node. You can only select destination edges or boundaries from the union of all source and destination edge or boundaries.

Periodicity Settings

Select —, , , , or .

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For the displacements and rotations on the destination are set equal to their counterparts on the source; u(xd) = u(xs) and a(xd) = a(xs). If the source and destination objects are rotated with respect to each other, a transformation is performed using the selected coordinate systems, so that corresponding components of the degrees of freedom are connected.

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For the displacements and rotations on the destination are set equal to their counterparts on the source but with the sign reversed; u(xd) = −u(xs) and a(xd) = −a(xs). If the source and destination objects are rotated with respect to each other, a transformation is performed using the selected coordinate systems, so that corresponding components of the degrees of freedom are connected.

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For enter a kF. This is the wave number vector for the excitation.

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For the settings differ slightly between the Plate and Shell interfaces.
In either case, enter an for the mode to be studied. It can vary from 0 to N/2, where N is the total number of sectors on a full revolution.


	In the Plate interface, choose how to define the sector angle that the geometry represents using the Sector angle list. If Automatic is selected, the program attempts to find out how many full repetitions of the geometry there will be on a full revolution. If User defined is selected, enter a value for the sector angle θS.


	In the Shell interface, enter the Axis direction vector, tc, if any point on the edge selection is located on the cyclic symmetry axis. The orientation of the cyclic symmetry axis is then needed for eliminating conflicting constraints. This setting is only relevant in 3D. You must always enter a value for the sector angle θS.

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For select the check box for any of the displacement or rotation components as needed. Then for each selection, choose the — or . Each selected displacement component will be connected by ui(xd) = ui(xs) or ui(xd) = −ui(xs). Each selected rotation component will be connected by ai(xd) = ai(xs) or ai(xd) = −ai(xs) If the source and destination objects are rotated with respect to each other, a transformation is performed using the selected coordinate systems so that corresponding components of the degrees of freedom are connected.

Constraint Settings

To display this section, click the button (

) and select in the dialog box.

In the COMSOL Multiphysics Reference Manual:

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Constraint Reaction Terms

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Weak Constraints

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Constraint Settings

Orientation of Source

To display this section, click the button (

) and select in the dialog box. For information about the section, see Orientation of Source and Destination in the COMSOL Multiphysics Reference Manual.

Orientation of Destination

This section appears if the setting for in the section is changed from the default value, , and is selected in the dialog box. For information about the section, see Orientation of Source and Destination in the COMSOL Multiphysics Reference Manual.

Mapping Between Source and Destination

For information about the section, see Mapping Between Source and Destination in the COMSOL Multiphysics Reference Manual.

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Cyclic Symmetry and Floquet Periodic Conditions in the Structural Mechanics Theory chapter.

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Orientation of Source and Destination in the COMSOL Multiphysics Reference Manual.


	Vibrations of an Impeller: Application Library path Structural_Mechanics_Module/Dynamics_and_Vibration/impeller

Location in User Interface

Context Menus

Ribbon

Physics tab with selected: