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


Geometry
---------

We consider a slender structure with a length :math:`0.25m` and a section :math:`0.05m\ast 0.03m`.


.. image:: images/10000000000004F200000251BEE5495EA3EDE7FB.png
    :width: 6.3374in
    :height: 2.9681in


.. _RefImage_10000000000004F200000251BEE5495EA3EDE7FB.png:


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

The material is isotropic elastic whose properties are:


* Young's module :math:`E=2.1{10}^{11}\mathit{Pa}`


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


* Density :math:`\rho =7800\mathit{kg}/\mathit{m³}`


* Hysteretic damping :math:`\eta =0.01`


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

We impose a zero displacement on the abscissa face :math:`y=0.25m`

To calculate the harmonic response, a vertical point excitation of amplitude :math:`(1+\mathrm{0.5j})/2` is applied to the coordinate point :math:`(0m\mathrm{,0}.1375m,0.03m)`.