2. Benchmark solution#
2.1. Calculation method#
The reference is given by the code CADYRO [bib1] for beam elements with variable cross section.
Moreover, the values resulting from the modeling using beam elements with a variable section (Modeling A) are framed by those obtained by those obtained from:
B modeling, approximating the exact solution by lower values. This is equivalent to assigning to each element the**constant circular section**with a diameter equal to the diameter of the rotor studied**in line with the initial node* of the element.
C modeling, approaching the exact solution by higher values. This consists in assigning to each element the**constant circular section**with a diameter equal to the diameter of the rotor studied* in line with the final node** of the element.
The B and C models are then equivalent (in the sense of the limit) to the A modeling when the number of elements used by them tends to infinity. In the present case, 2000 beam elements with a constant circular cross section are used.
2.2. Reference quantities and results#
The reference quantity is the frequency of the modes at rest and for a rotation speed of 4000 \(\mathrm{tr}/\mathrm{mn}\). The number of modes calculated is 12.
Frequency Number |
Rotation speed ( \(\mathit{tr}/\mathit{mn}\) ) |
Cadyro calculation with a variable-section tree \(F\) ( \(\mathit{Hz}\) ) |
1 |
0 |
332.14 |
4000 |
331.51 |
|
2 |
0 |
332.14 |
4000 |
334.10 |
|
3 |
0 |
1193.81 |
4000 |
1196.30 |
|
4 |
0 |
1193.81 |
4000 |
1202.05 |
|
5 |
0 |
1607.19 |
4000 |
1607.19 |
|
6 |
0 |
2291.51 |
4000 |
2304.73 |
|
7 |
0 |
2291.51 |
4000 |
2312.08 |
|
8 |
0 |
2512.22 |
4000 |
2512.22 |
|
9 |
0 |
3160.39 |
4000 |
3160.39 |
|
10 |
0 |
3520.23 |
4000 |
3516.43 |
|
11 |
0 |
3520.23 |
4000 |
3524.02 |
|
12 |
0 |
4724.14 |
4000 |
4724.14 |
2.3. Bibliographical references#
Code validation file CADYRO 2.0, finite element software for predicting the dynamic behavior of rotors, H-P60-1994-04877-FR.