Wave number in cyclic symmetry solutions (Simcenter Samcef)

Wave number

Let’s consider a cyclic structure composed of N sectors (or Segments) repeating the same reference sector.

Each sector is in contact with only two other identical sectors (except, possibly, on the axis around which the sectors are equally distributed).

This means that for a geometry defined at the revolution angle α, it is identical to the one at angle α + n β, where β equals 2*pi/N and n is an index (0, 1, . . . ,N − 1) called the Wave Number or nodal diameter.

After the structure geometry is defined from α to α + β, the rest of the structure can be obtained by simply repeating rotations of that block by a magnitude of β.

The Wave Number has a simple physical interpretation: when a free wave propagates through a structure, eiβ is the ratio of the displacements of two homologous points located on the contour of each sector.

In a Modal Analysis, you have to specify the Wave Number. A zero value corresponds to the computation of the axisymmetric modes of the model. One Wave Number value can only be defined in a single modal solution.

In a Linear Static Analysis, it is always zero.

For more information, see the cyclic symmetry page in the Simcenter Samcef solver documentation.

Dynamical problem

The dynamical problem of the complete cyclic structure can be exactly transform into N reduced problems (corresponding to each wave number n) on the reference sector with appropriate inter-sector boundary conditions.

If the reference sector has a u0l displacement for its left inter-sector degrees of freedom and a u0r displacement for its right inter-sector degrees of freedom, the displacement of the left degrees of freedom for the wave number n can be expressed as:

u0l = e-2iPI*n/N u0r.

Where do I find it?

Application	Pre/Post
Prerequisite	A Simulation file as the work part and displayed partSimcenter Samcef as the specified solverStructural as the specified analysis typeModal Analysis as the specified solution type
Location in dialog box	Analysis page→Cyclic Symmetry group→Activate Cyclic Symmetry check box

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Solution dialog box (Simcenter Samcef Modal Analysis)

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Wave number in cyclic symmetry solutions (Simcenter Samcef), Simcenter 3D 2021.1 Series

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