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


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


Geometry
---------

Coordinates of points expressed in meters:

 :math:`A:(0.0,0.0)`

 :math:`B:(0.35,0.0)`

 :math:`C:(0.35,0.6)`

 :math:`D:(0.0,0.6)`


Elastic properties of the material
---------------------------------


* :math:`E=1.8\times {10}^{11}\mathrm{Pa}` Young's module


* :math:`\nu =0.3` Poisson's Ratio


* :math:`\rho =7800.0{\mathrm{kg.m}}^{-3}` Density


* :math:`\alpha =3\times {10}^{-5}s`


* :math:`\beta =0.001{s}^{-1}`

The coefficients :math:`\alpha` and :math:`\beta` make it possible to build a viscous damping matrix that is proportional to the stiffness and to the mass :math:`[C]=\alpha [K]+\beta [M]`.


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


*
    * Embedding on the :math:`\mathit{AD}` side

:math:`\mathrm{DX}=0.0m`, :math:`\mathrm{DY}=0.0m`


*
    *
        * The :math:`\mathit{BC}` side is subject to a harmonic pressure of amplitude :math:`p\mathrm{=}{10}^{5}\mathit{Pa}` at a frequency :math:`f=1500\mathrm{Hz}`


*