2. Benchmark solution#
2.1. Calculation method used for the reference solution#
A direct modal calculation is used to obtain the natural frequencies modified by the fluid around the spheres.
The two spheres are deduced by a vector translation of components \((\mathrm{2,}0.,0.)\) and for a rotation of nautical analyses \((90.,0.,90.)\), which makes it possible to consider building a generalized model on the 1st sphere. It is possible to perform the same modal calculation with fluid/structure coupling using dynamic substructuring. The direct calculation taking into account the added mass leads to the following natural frequencies of the submerged system:
\({f}_{1}=\) |
|
\({f}_{2}=\) |
|
\({f}_{3}=\) |
|
\({f}_{4}=\) |
|
\({f}_{5}=\) |
|
\({f}_{6}=\) |
|
2.2. Benchmark results#
Direct modal calculation by*Code_Aster*.
2.3. Uncertainty about the solution#
The uncertainties in the solution are linked to the discretization of the fluid/structure interface and to the invariance of the mesh by rotation of nautical angles \((90°,0°,90°)\).