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


Geometry
---------


.. image:: images/1000095400002C57000008E3C131B213B2275130.svg
    :width: 571
    :height: 114


.. _RefImage_1000095400002C57000008E3C131B213B2275130.svg:

The system consists of a circular piston vibrating in contact with an annular fluid column ending in a free surface:

Length: :math:`1m`

width: :math:`0.03m`

height: :math:`0.025m`

the axis of revolution is axis :math:`\mathrm{OY}` of the coordinate system. :math:`\mathrm{OX}` refers to the radial axis.


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

Structure: steel - elastic material

:math:`E={2.10}^{13}\mathrm{Pa}`

:math:`\nu =0.3`

:math:`{\rho }_{s}=7800\mathrm{kg}/{m}^{3}`

The spring has a stiffness per radian of :math:`K=\frac{{10}^{5}}{2\pi }N/m/\mathrm{rad}`

Fluid: equivalent thermal material

:math:`\lambda =1.`

:math:`{\rho }_{f}{C}_{p}=1000.`


Boundary conditions and loads
-------------------------------------

On the structure side: the :math:`\mathrm{DX}` degree of freedom of all the nodes in the structure is locked: DX: 0.0

On the fluid side: zero pressure (i.e. temperature) is imposed on the nodes of the free surface.