Periodic Condition

Use a to prescribe that the displacements on two different sets of boundaries with the same geometrical shape are related, as in a periodic structure.

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 between displacements and 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 and options are available only with some COMSOL products (see http://www.comsol.com/products/specifications/).

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

Boundary Selection

Select both the source and destination boundaries.

The software automatically identifies the boundaries as either source boundaries or destination boundaries. This works fine for cases like opposing parallel boundaries. In more general cases, use the subnode to specify the boundaries which constitute the destination. By default this node contains the selection that COMSOL Multiphysics has identified.

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

Periodicity Settings

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

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For the displacements on the destination are set equal to the displacements on the source;

. If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding displacement components are connected.

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For the displacements on the destination are set equal to the displacements on the source with the sign reversed;

. If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding displacement components are connected.

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

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For chose how to define the sector angle that the geometry represents using . If is selected, the program attempts to find out how many full repetitions of the geometry there will be on a full revolution. If is selected, enter a value for the sector angle θS. In both cases, 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.

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For select the check box for any of the displacement components as needed. Then for each selection, choose the — or . Each selected displacement component will be connected by

respectively. If the source and destination boundaries are rotated with respect to each other, a transformation is automatically performed, so that corresponding displacement components are connected.