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 hollow cylinder with a length :math:`L\mathrm{=}\mathrm{0,254}m`, a radius :math:`R\mathrm{=}\mathrm{0,09525}m` and a thickness :math:`\mathit{Ep}\mathrm{=}\mathrm{0,03810}m`.


.. image:: images/100002000000019F0000015BFCD94A64B62AA3DA.png
    :width: 2.4701in
    :height: 1.8953in


.. _RefImage_100002000000019F0000015BFCD94A64B62AA3DA.png:

Image 1.1-1: Hollow cylinder geometry




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

The cylinder has a density of :math:`\rho \mathrm{=}7860\mathit{kg}\mathrm{/}{m}^{3}`.

The Young's modulus is :math:`E\mathrm{=}207.{10}^{9}N{m}^{\mathrm{-}2}` and the Poisson's ratio is :math:`\nu \mathrm{=}\mathrm{0,28}`.




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

The cylinder is in a freestanding configuration. It is stationary or rotating at 1000, 2000 and 3000 rpm.