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


Geometry
---------


.. image:: images/100000000000021F000002179DF7AEA1813CDC49.png
    :width: 2.8075in
    :height: 2.8543in


.. _RefImage_100000000000021F000002179DF7AEA1813CDC49.png:

Inner radius: :math:`{R}_{i}=0.1m`

Outside radius: :math:`{R}_{e}=0.2m`

Thickness: :math:`t=0.001m`


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

:math:`E={2.10}^{11}\mathrm{Pa}`

:math:`\nu =0.3`

:math:`\rho =7\mathrm{800kg}/{m}^{3}`


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

Hub mounting

For all points :math:`r={R}_{i}`, :math:`u=v=w=0.`, and :math:`{\theta }_{x}={\theta }_{y}={\theta }_{z}=0`.


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

Not applicable for modal analysis.