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


Geometry
---------


.. image:: images/100002000000032B0000023B45BC70DBDBD242CB.png
    :width: 3.2917in
    :height: 1.9791in


.. _RefImage_100002000000032B0000023B45BC70DBDBD242CB.png:

Dimensions of pad :math:`(m)`:

         length (according to :math:`x`): :math:`0.35`

         width (according to :math:`y`): :math:`0.25`

         thickness (according to :math:`z`): :math:`0.01`


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 proportional to the stiffness and to the mass :math:`[C]=\alpha [K]+\beta [M]`.


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


*
    * Embedding the side faces


*
    *
        * Harmonic pressure of amplitude :math:`p={10}^{5}\mathrm{Pa}` at a frequency :math:`f=1500\mathrm{Hz}` on the upper side