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

The objective of this test case is to validate the 3D gyroscopic modeling of a full cylinder (options MECA_GYRO and RIGI_ROTA) in Code_Aster.

The results obtained by modeling Code_Aster are compared with those obtained in ANSYS.




Geometry
---------

We consider a solid cylinder of length :math:`L\mathrm{=}\mathrm{0,4}m`, and radius :math:`R\mathrm{=}\mathrm{0,01}m`.


.. image:: images/10000200000002D900000158A703A5D7842F4C00.png
    :width: 2.9217in
    :height: 1.628in


.. _RefImage_10000200000002D900000158A703A5D7842F4C00.png:

Image 1.1-1: Solid cylinder geometry




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

The cylinder has a density of :math:`\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}`.

The Young's modulus is :math:`E\mathrm{=}200.{10}^{9}N{m}^{\mathrm{-}2}` and the Poisson's ratio is :math:`\nu \mathrm{=}0`.




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

The movements in X, Y and Z of the middle nodes of the sections at the ends of the cylinder are blocked.

It is stationary or rotating at the following speeds: 10000, 20000, 20000, 40000, 60000, 80000 and 100000 rpm.