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The Continuity, Antiperiodicity, and User defined 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 Floquet periodicity 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 Cyclic symmetry 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.
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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.
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In the 2D axisymmetry, Edge Selection is replaced by Point Selection. In the Plate interface, Edge Selection is replaced by Boundary Selection.
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For Continuity 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 Antiperiodicity 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 Floquet periodicity enter a k-vector for Floquet periodicity kF. This is the wave number vector for the excitation.
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For Cyclic symmetry the settings differ slightly between the Plate and Shell interfaces.
In either case, enter an Azimuthal mode number 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.
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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.
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For User defined select the check box for any of the displacement or rotation components as needed. Then for each selection, choose the Type of periodicity — Continuity or Antiperiodicity. 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.
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In the COMSOL Multiphysics Reference Manual:
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Vibrations of an Impeller: Application Library path Structural_Mechanics_Module/Dynamics_and_Vibration/impeller
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