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


Geometry
---------

A rotor model supported by 2 bearings (nodes :math:`\mathrm{B1}` and :math:`\mathrm{B2}` in the figure below), whose stiffness and damping matrices are non-symmetric. It is composed of 3 disks, and 3 shaft sections.


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.. image:: images/Object_1.svg
    :width: 580
    :height: 215


.. _RefImage_Object_1.svg:

**Figure** 1.1-a **-a: Rotor model with 2 discs and 2 asymmetric bearings**


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

The geometric and material characteristics are listed in the following table.


+--------+-------------------+------------------------------+----------------------------------------------+---------------------------------------------+
|Material                    |:math:`E={2.10}^{11}N/{m}^{2}`|:math:`\rho =7800\mathrm{kg}/{m}^{3}`         |:math:`\nu =0.3`                             |
+--------+-------------------+------------------------------+----------------------------------------------+---------------------------------------------+
|Disc    |:math:`\mathrm{D1}`|:math:`M=3.5\mathrm{kg}`      |:math:`{I}_{D}=3.5{10}^{-3}\mathrm{kg}{m}^{2}`|:math:`{I}_{P}={7.10}^{-3}\mathrm{kg}{m}^{2}`|
+--------+-------------------+------------------------------+----------------------------------------------+---------------------------------------------+
|        |:math:`\mathrm{D2}`|:math:`M=3.0\mathrm{kg}`      |:math:`{I}_{D}=3.0{10}^{-3}\mathrm{kg}{m}^{2}`|:math:`{I}_{P}={6.10}^{-3}\mathrm{kg}{m}^{2}`|
+--------+-------------------+------------------------------+----------------------------------------------+---------------------------------------------+


Boundary conditions
----------------------

To block rigid body movements in direction :math:`Z`, we block the degree of freedom :math:`\mathit{DZ}` at the level node :math:`\mathrm{B1}`.