Reference problem
=====================


Geometry
---------


.. image:: images/1000246E0000267300000F4C2D8EFD6EA689E23E.svg
    :width: 495
    :height: 197


.. _RefImage_1000246E0000267300000F4C2D8EFD6EA689E23E.svg:

:math:`{L}_{a}=0.075`, :math:`{L}_{s}=0.025`, :math:`{L}_{e}=0.05m`

constant square section, :math:`a=0.05m` or circular cross section (in the axisymmetric case) constant with radius :math:`R=a=0.05m`.


Material properties
------------------------


.. csv-table::

    "solid: :math:`E={2.10}^{11}\mathrm{Pa}` "," :math:`{\rho }_{s}=7800\mathrm{kg}/{m}^{3}` "," :math:`\nu =0.3`"
    "air: :math:`{c}_{a}=340m/s` "," :math:`{\rho }_{a}=1.2\mathrm{kg}/{m}^{3}` ", ""
    "water: :math:`{c}_{e}=1400m/s` "," :math:`{\rho }_{e}=1000\mathrm{kg}/{m}^{3}` "," :math:`c=\mathrm{célérité}\mathrm{du}\mathrm{son}`"


:math:`c=` Speed of sound in the fluid


Boundary conditions and loading
------------------------------------


* For all points :math:`M` on face :math:`(\mathrm{M1}\mathrm{M2}\mathrm{M3}\mathrm{M4})` the pressure and the displacement potential are zero (free surface condition),


* for the points :math:`P` of the solid, we block all the degrees of freedom except the translation in :math:`x` so that this solid behaves like a piston along the axis :math:`x`.