3. Modeling A#
3.1. Characteristics of modeling#
The modeling of elasto-acoustic beams is in formulation \(u,\theta ,p,\phi\).
It is achieved by assigning elements PHENOMENE = “MECANIQUE”, MODELISATION = “FLUI_STRU” to SEG2 meshes (segments with 2 nodes).
The circular cross-section characteristics are assigned to the elements:
outer radius |
\({R}_{\mathit{ext}}=\mathrm{0,100}m\) |
|
thickness |
\(\mathit{ep}=\mathrm{0,010}m\) |
cf. [§1.1] |
We also assign to these elements a mixed behavior material at the same time ELAS:
Young’s module |
\(E=\mathrm{1,0}.1010\mathit{Pa}\) |
|
Poisson’s ratio |
\(\nu =\mathrm{0,3}\) |
|
density |
\({\rho }_{s}=1000\mathit{kg}/{m}^{3}\) |
and FLUIDE:
speed |
\(c=1000m/s\) |
|
density |
\({\rho }_{f}=1000\mathit{kg}/{m}^{3}\) |
cf. [§1.2] |
The degrees of freedom (DDL) of translation in \(y\) and \(z\) (DY and DZ) and all the degrees of freedom of rotation (DRX, DRY and DRZ) of all the nodes are blocked.
In order to embed the \(A\) end of the pipe, the degree of freedom of translation is also blocked in \(x\) (DX) of the node \(\mathit{NO1}\).
For the fluid the reservoir condition at the \(A\) end is imposed by PRES = 0. and PHI = 0. at the node \(\mathit{NO1}\).
3.2. Characteristics of the mesh#
The total number of nodes used for this mesh is 26.
The stitches are 25 in number and of type SEG2.
The mesh file is in ASTER format.
3.3. Calculus#
We want to validate the elasto-acoustic beam elements.
The frequency of the first axially coupled mode is calculated with operator CALC_MODES.
3.4. Tested values#
The test focuses on the frequency of the first coupled axial mode of the fluid-containing pipe.
The tolerance for relative deviation from the analytical value is 0.1%.
Mode Number |
Analytical Value |
1 |
Non-regression value |
3.5. note#
The reference values are both the analytical values and also those obtained by Code_Aster during the retrieval of the test case, which will therefore make it possible to verify the subsequent non-regression of the code during its evolution.