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


Geometry
---------


.. image:: images/10000000000001F20000018ECF16B248AB825092.png
    :width: 2.5591in
    :height: 2.0429in


.. _RefImage_10000000000001F20000018ECF16B248AB825092.png:



**Figure 1.1 Problem geometry**

Tank dimensions:


* height: :math:`\text{H}=0.3048\text{m}`


* mean radius: :math:`\text{R}=0.076073\text{m}`


* shell thickness: :math:`\text{e}=0.254\times {10}^{-3}\text{m}`

The free surface is located at ordinate :math:`Z=\text{H}`. It is perpendicular to the :math:`Z` axis.


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

The properties of the fluid filling the cavity are as follows:


.. csv-table::

    "Sound speed", ":math:`{c}_{F}=1400{\text{m.s}}^{-1}`"
    "Density", ":math:`{\rho }_{F}=1000{\text{kg.m}}^{-3}`"


The properties of the shell are as follows:


.. csv-table::

    "Young's module", ":math:`E=2.06\times {10}^{11}\text{Pa}`"
    "Poisson's Ratio", ":math:`\nu =0.3`"
    "Density", ":math:`{\rho }_{S}=7850.0{\text{kg.m}}^{-3}`"



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

Embedding at the base:


.. math::
: label: EQ-None

    \ textrm {At any point such as}
    Z=0

Fluid subject to a gravity field:


.. csv-table::

    "At any point in the fluid", "Gravity :math:`g=9.81{\text{m/s}}^{2}` next :math:`Z`"