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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


* Beam:

:math:`L=0.9m`

:math:`r=0.025m`

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


* Beam


* :math:`E=2.06\mathrm{E11}\mathrm{Pa}` Young's module


* :math:`\nu =0.` Poisson's ratio


* :math:`\rho =7800.\mathrm{kg}/{m}^{-3}` Density


* Disc


    * :math:`m=0.03829\mathrm{Kg}`


    * mass inertia tensor


    * :math:`{I}_{\mathrm{yy}}=1.8\times {10}^{-6}{\mathrm{Kg.m}}^{2}`


    * :math:`{I}_{\mathrm{yy}}=1.8\times {10}^{-6}{\mathrm{Kg.m}}^{2}`


    * :math:`{I}_{\mathrm{zz}}=1.8\times {10}^{-6}{\mathrm{Kg.m}}^{2}`


    * :math:`{I}_{\mathrm{xy}}={I}_{\mathrm{yz}}={I}_{\mathrm{xz}}=0.`


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

Mandatory trips :math:`(m)`:

Points :math:`A` and :math:`B`: :math:`\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=0`

rotation speed:

:math:`\omega =10000\mathrm{tr}/\mathrm{mn}`