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


Geometry
---------


.. image:: images/100000000000047900000197F2D7825618F4A457.png
    :width: 6.6425in
    :height: 2.4484in


.. _RefImage_100000000000047900000197F2D7825618F4A457.png:

:math:`L=50m` :math:`l=5m`

fluid thickness :math:`e=0.5m`

plate thickness :math:`h=0.5m`


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

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

     Structure: :math:`{\rho }_{s}\mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}`, :math:`E\mathrm{=}2.1{10}^{11}\mathit{Pa}`, :math:`\nu \mathrm{=}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, a normal speed of, the fluid inlet speed :math:`{\overrightarrow{V}}_{0}` being in the opposite direction to the normal inlet (by analogy with thermal analysis, a normal heat flow equivalent to :math:`–4` is imposed),


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


* In :math:`x=\frac{e}{2}`, condition :math:`{\phi }_{1}={\phi }_{2}=0` is imposed, which corresponds to a zero flow rate through the upper fluid wall.

Structure:


* the plate is subjected to an imposed displacement corresponding to a first mode of flexure [bib2] _:

:math:`{X}_{1}\mathrm{=}\text{sin}\frac{\pi y}{L}\text{}`