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


Geometry
---------


.. image:: images/1000000000000306000002F4DFDF82EB0FB3D248.png
    :width: 4.1339in
    :height: 4.028in


.. _RefImage_1000000000000306000002F4DFDF82EB0FB3D248.png:



**Figure 1.1 Problem geometry and loading system**

Parallelipipedic cavity:


* length: :math:`{l}_{x}=1.0m`


* height: :math:`{l}_{y}=1.0m`


* width: :math:`{l}_{z}=2.0m`

Coordinates of the points:


* :math:`\mathit{N1}`: :math:`x=0.6`, :math:`y=0.4`, :math:`z=0.0`


* :math:`\mathit{N2}`: :math:`x=0.5`, :math:`y=0.5`, :math:`z=1.0`


* :math:`\mathit{N3}`: :math:`x=0.5`, :math:`y=0.5`, :math:`z=2.0`


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

The material properties of the fluid are those of air:


.. csv-table::

    ":math:`{c}_{F}=340{\text{m.s}}^{-1}` ", "Sound speed"
    ":math:`{\rho }_{F}=1.2{\text{kg.m}}^{-3}` ", "Density"


The material properties of the plate are those of steel:


.. csv-table::

    ":math:`E=2.1\times {10}^{11}\text{Pa}` ", "Young's module"
    ":math:`\nu =0.3` ", "Poisson's ratio"
    ":math:`{\rho }_{S}=7800.0{\text{kg.m}}^{-3}` ", "Density"
    ":math:`t=0.005\text{m}` ", "Thickness"



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

Imposed displacement:

.. csv-table::

    "Plate wall", ":math:`\mathit{DX}=0`, :math:`\mathit{DY}=0`, :math:`\mathit{DZ}=0`"


Imposed loading:

.. math::
: label: EQ-None

    \ textrm {Point}
    \ mathit {N1}