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


Geometry
---------


.. image:: images/100000000000015F000000AFD4E802432478F73C.jpg
    :width: 3.5098in
    :height: 1.75in


.. _RefImage_100000000000015F000000AFD4E802432478F73C.jpg:

**Modeling:**


.. csv-table::

    "", "Mass (:math:`\mathrm{kg}`)", ":math:`{I}_{\mathrm{xx}}` (:math:`{\mathrm{kg.m}}^{2}`)", ":math:`{I}_{\mathrm{yy}}={I}_{\mathrm{zz}}` (:math:`{\mathrm{kg.m}}^{2}`)"
    "Disc :math:`{D}_{1}` ", "14.580130", "0.1232021", "0.6463858"
    "Disk :math:`{D}_{2}` ", "45.945793", "0.97634809", "0.4977460"
    "Disc :math:`{D}_{3}` ", "55.134951", "1.1716177", "0.6023493"


Table 1.1-1: Characteristics of disks

**Beam length:**

:math:`{L}_{1}=\mathrm{AB}=0.2m`

:math:`{L}_{2}=\mathrm{BC}=0.3m`

:math:`{L}_{3}=\mathrm{CD}=0.5m`

:math:`{L}_{4}=\mathrm{DE}=0.3m`

**Circular section:**

Diameter: :math:`D=0.1m`


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

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

:math:`\nu =0.3`

:math:`\rho =7800\mathrm{kg}/{m}^{3}`


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

Elastic supports with viscous damping in :math:`A` and :math:`E`

:math:`{K}_{\mathrm{yy}}={5.10}^{7}{\mathrm{N.m}}^{-1}`; :math:`{K}_{\mathrm{zz}}={7.10}^{7}{\mathrm{N.m}}^{-1}`; :math:`{K}_{\mathrm{yz}}={K}_{\mathrm{zy}}=\mathrm{0 }`

:math:`{C}_{\mathrm{yy}}={5.10}^{2}N/({\mathrm{m.s}}^{-1})`; :math:`{C}_{\mathrm{zz}}={7.10}^{2}N/({\mathrm{m.s}}^{-1})`; :math:`{C}_{\mathrm{yz}}={C}_{\mathrm{zy}}=0`