2. Benchmark solution#
2.1. Calculation method used for the reference solution#
We are specifically interested in natural flexural modes. The frequencies are compared to those obtained numerically using the SAMCEF software. The calculation technique used is a direct cyclic symmetry method, without recourse to a modal basis.
2.2. Benchmark results#
The modal analysis was carried out with three meshes of different fineness. The table below provides the first four double frequencies corresponding to each of the three meshes for different rotation speeds.
Modes |
Natural frequencies (\(\mathit{Hz}\)) Rotation speed: \(0{\text{rd.s}}^{-1}\) |
||
160 elements |
540 elements |
1280 elements |
|
1.2 |
\(442.1\) |
\(440.3\) |
\(438.6\) |
3.4 |
\(1452.\) |
\(1436.\) |
\(1428.\) |
5,6 |
\(3342.\) |
\(3311.\) |
\(3297.\) |
7.8 |
\(4855.\) |
\(4828.\) |
\(4812.\) |
Number of modes |
Natural frequencies (\(\mathit{Hz}\)) Rotation speed: \(2000{\text{rd.s}}^{-1}\) |
||
160 elements |
540 elements |
1280 elements |
|
1.2 |
\(409\) |
\(406.8\) |
\(404.9\) |
3.4 |
\(1431.\) |
\(1414.\) |
\(1407.\) |
5,6 |
\(3335.\) |
\(3304.\) |
\(3290.\) |
7.8 |
\(4852.\) |
\(4824.\) |
\(4809.\) |
The reference results used in the models in this test are those of the 160-element mesh.
2.3. Uncertainty about the solution#
Digital solution obtained by external software.