Periodic Condition

Use a to prescribe that the displacements and rotations on two different sets of edges with the same geometrical shape are related, as in a periodic structure. In the Plate interface the connection is between boundaries rather than edges as is the case in the Shell interface.

Several different types of periodicity properties of the solution can be prescribed using this boundary condition.

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

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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 which are identical when rotated around a common axis, like in a fan.

The two sets of edges 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, 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

Select both the source and destination edges.

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, use the subnode to 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 geometry edges for the matching to work properly.


	In the Plate interface, Edge Selection is replaced by Boundary Selection.

Periodicity Settings

With you select the form of periodicity that your solution should have.

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For the displacements and rotations on the destination are set equal to their counterparts on the source;

and

. 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;

and

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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, also 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.


	If any point on the edges having the periodic condition is located on the axis of cyclic symmetry, enter the Axis direction vector, tc. This orientation of the axis of cyclic symmetry is then needed for eliminating conflicting constraints. In the Shell interface, you always must 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

. Each selected rotation component will be connected by

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

In , select a coordinate system representing the orientation of the degrees of freedom on the source selection. The corresponding setting for the destination is given in the subnode.

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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:

Physics tab with node selected in the model tree: