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


Geometry
---------

We consider a beam of length :math:`L=\mathrm{7,62}m`, of rectangular cross section (:math:`\mathit{Hy}=\mathrm{0,0508}m` and :math:`\mathit{Hz}=\mathrm{0,0254}m`). It is oriented along the :math:`\mathit{Ox}` axis.


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

The material is isotropic elastic whose properties are:


* Young's modulus: :math:`E=\mathrm{206,8}{10}^{9}\mathrm{Pa}`


* Poisson's ratio: :math:`\nu =\mathrm{0,3}`


* density: :math:`\rho =\mathrm{7780,0}\mathrm{kg}/{m}^{3}`


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

The beam is embedded at each of its ends.

The load is a seismic excitation perpendicular to the direction of the beam, expressed in the form of an accelerogram. It is taken from a recording of the so-called El Centro earthquake (). The direction of the earthquake is axis :math:`\mathit{Oy}`. The sample is :math:`\mathrm{0,01}s`.


.. image:: images/100000000000034A00000253F4218E05A6F5E129.png
    :width: 6.3374in
    :height: 4.478in


.. _RefImage_100000000000034A00000253F4218E05A6F5E129.png:

Illustration 1: Accelerogram called "El Centro" taken over 2 s.

For modeling A, single-pressed excitation is considered: the same accelerogram is imposed at both ends of the beam.

For modeling B, a multi-press excitation is considered: the accelerogram imposed at both ends is the same as in mono-press but, in this case, at the opposite end it is applied with a delay of :math:`\mathrm{0,25}s` compared to the origin.


Initial conditions
--------------------

The beam is considered to be at rest before the earthquake arrives.