Modélisation A
==============


Caractéristiques de la modélisation
-----------------------------------

Modélisation DKT (QUAD4)


Caractéristiques du maillage
----------------------------

Nombre de nœuds: 3030

Nombre de mailles et types : 3000 QUAD4

(Le cercle est coupé en 30 segments)


Grandeurs testées et résultats
------------------------------

Tab. 2. Résultats de la modélisation A


+---------+----------------------------------+-----------------------------------+----------------------------------+
| **m=1** | **FF**                           | **SF**                            | **SS**                           |
|         +-----------+---------+------------+-----------+----------+------------+-----------+---------+------------+
|         | **Aster** | **Ref** | **%** diff | **Aster** | **Ref**  | **%** diff | **Aster** | **Ref** | **%** diff |
+---------+-----------+---------+------------+-----------+----------+------------+-----------+---------+------------+
| **n=2** | 657,335   | 654,216 | 0,48       | 657,938   | 657,308  | 0,10       | 667,023   | 663,543 | 0,52       |
+---------+-----------+---------+------------+-----------+----------+------------+-----------+---------+------------+
| **n=3** | 1858,85   | 1850,29 | 0,46       | 1859,73   | 1851,81  | 0,43       | 1865,40   | 1855,44 | 0,54       |
+---------+-----------+---------+------------+-----------+----------+------------+-----------+---------+------------+
| **n=4** | 3564,70   | 3547,66 | 0,48       | 3565,61   | 3549,113 | 0,46       | 3572,44   | 3552,95 | 0,55       |
+---------+-----------+---------+------------+-----------+----------+------------+-----------+---------+------------+
| **n=5** | 5767,42   | 5737,23 | 0,53       | 5768,30   | 5738,70  | 0,52       | 5775,67   | 5742,74 | 0,57       |
+---------+-----------+---------+------------+-----------+----------+------------+-----------+---------+------------+
| **n=6** | 8466,42   | 8416,32 | 0,60       | 8467,30   | 8417,79  | 0,59       | 8474,04   | 8421,97 | 0,62       |
+---------+-----------+---------+------------+-----------+----------+------------+-----------+---------+------------+


+---------+----------------------------------+----------------------------------+--------+
| **m=1** | **SC**                           | **CC**                           |        |
|         +-----------+---------+------------+-----------+---------+------------+--+--+--+
|         | **Aster** | **Ref** | **%** diff | **Aster** | **Ref** | **%** diff |  |  |  |
+---------+-----------+---------+------------+-----------+---------+------------+--+--+--+
| **n=2** | 675,59    | 671,113 | 0,67       | 690,073   | 687,249 | 0,41       |  |  |  |
+---------+-----------+---------+------------+-----------+---------+------------+--+--+--+
| **n=3** | 1866,57   | 1856,45 | 0,54       | 1868,14   | 1858,30 | 0,53       |  |  |  |
+---------+-----------+---------+------------+-----------+---------+------------+--+--+--+
| **n=4** | 3572,85   | 3553,29 | 0,55       | 3573,32   | 3553,91 | 0,55       |  |  |  |
+---------+-----------+---------+------------+-----------+---------+------------+--+--+--+
| **n=5** | 5775,87   | 5742,87 | 0,57       | 5776,09   | 5743,21 | 0,57       |  |  |  |
+---------+-----------+---------+------------+-----------+---------+------------+--+--+--+
| **n=6** | 8474,16   | 8422,00 | 0,62       | 8474,27   | 8422,24 | 0,62       |  |  |  |
+---------+-----------+---------+------------+-----------+---------+------------+--+--+--+


Remarques
---------

On n’a pas trouvé le mode propre pour :math:`n=1` et :math:`m=1` .

Grâce à la symétrie de la structure du tuyau, on observe que les modes propres de :math:`n=2-6` et :math:`m=1` apparaissent toujours en couple.