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


Geometry
---------


.. image:: images/10000D0400001A9000001565F27CEA929BB2B41A.svg
    :width: 280
    :height: 231


.. _RefImage_10000D0400001A9000001565F27CEA929BB2B41A.svg:

**Two cylinders separated by incompressible fluid:**

inner radius :math:`{R}_{1}=1.0m` outer radius :math:`{R}_{2}=1.1m`


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

**Fluid:**

Water: :math:`{\rho }_{0}=1000.0{\mathrm{Kg.m}}^{-3}`

**Solid:**

Steel: :math:`{\rho }_{S}=7800.0{\mathrm{Kg.m}}^{-\mathrm{3 }}`; :math:`E=2.E11\mathrm{Pa}`; :math:`\nu =0.3`

**Spring connecting the piston to the solid:**

A discrete element is placed on mesh POI1 in the center of the :math:`{\Gamma }_{1}` stiffness cylinder

.. image:: images/Object_8.svg
    :width: 280
    :height: 231


.. _RefImage_Object_8.svg:

and two discrete elements on mesh POI1 on the cylinder :math:`{\Gamma }_{2}` at the level of the axis :math:`\mathrm{Ox}` whose stiffness is equal

.. image:: images/Object_10.svg
    :width: 280
    :height: 231


.. _RefImage_Object_10.svg:

.


.. csv-table::

    "Discrete elements of the K_T_D_L type:", ":math:`\mathrm{K1}=(1.E7,1.E7,1.E7)N/m`"
    "", ":math:`\mathrm{K2}=(5.E6,5.E6,5.E6)N/m`"



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

Pressure is imposed (i.e. by thermal analogy a zero temperature [:ref:`R4.07.03 <R4.07.03>`]) at any node in the fluid.

A zero displacement of the cylinders is imposed according to :math:`\mathrm{Oy}`.


Initial conditions
--------------------

Not applicable for added mass calculation and modal analysis.