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


Geometry
---------


.. image:: images/Object_1.svg
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    :height: 197


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:math:`L=50m`

:math:`I=5m`

fluid thickness :math:`e=0.5m`

plate thickness :math:`h=0.5m`

The coordinate :math:`\mathrm{Oxyz}` is located at a distance of :math:`\frac{e}{2}` from the plate


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

Fluid: density :math:`\rho =1000{\mathrm{kg.m}}^{-3}` (water).

Structure: :math:`{\rho }_{s}=7800\mathrm{kg}/{m}^{3}`; :math:`E=2.1{10}^{11}\mathrm{Pa}`; :math:`\nu =0.3` (steel).


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

Fluid:


* to simulate the permanent flow, a normal speed of :math:`–4m/s` is imposed on the fluid inlet face (by thermal analysis, a normal heat flow equivalent to —4 is imposed),


* To calculate the fluid disturbance caused by the movement of the external cylinder, a Dirichlet boundary condition is imposed at a fluid node.


* we impose in

    .. image:: images/Object_9.svg
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        :height: 197


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The condition

    .. image:: images/Object_10.svg
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which corresponds to a zero flow through the upper fluid wall.

Structure:


* the plate is subjected to a displacement corresponding to its first two modes of flexure [:ref:`bib2 <bib2>`]:


.. image:: images/Object_11.svg
    :width: 655
    :height: 197


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