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


Geometry
---------


.. image:: images/100000000000020F000000CCDA4B2773532EEC71.jpg
    :width: 5.4898in
    :height: 2.1252in


.. _RefImage_100000000000020F000000CCDA4B2773532EEC71.jpg:

Beam cross sections:


* support frame


.. csv-table::

    ":math:`\mathrm{S1}`:", ":math:`A=1.2061{10}^{-2}{m}^{2}` "," :math:`{I}_{z}=2.3681{10}^{-5}{m}^{4}`"
    ":math:`\mathrm{S5}`:", ":math:`A=1.4621{10}^{-2}{m}^{2}` "," :math:`{I}_{z}=2.8709{10}^{-5}{m}^{4}`"
    ":math:`\mathrm{S9}`:", ":math:`A=1.5530{10}^{-2}{m}^{2}` "," :math:`{I}_{z}=3.0493{10}^{-5}{m}^{4}`"



* insulating columns


.. csv-table::

    ":math:`\mathrm{S2}`:", ":math:`A=3.1428{10}^{-2}{m}^{2}` "," :math:`{I}_{z}=4.5070{10}^{-5}{m}^{4}`"
    ":math:`\mathrm{S6}`:", ":math:`A=3.2592{10}^{-2}{m}^{2}` "," :math:`{I}_{z}=4.6738{10}^{-5}{m}^{4}`"
    ":math:`\mathrm{S10}`:", ":math:`A=3.3416{10}^{-2}{m}^{2}` "," :math:`{I}_{z}=4.7927{10}^{-5}{m}^{4}`"



* fittings


.. csv-table::

    ":math:`\mathrm{S3},\mathrm{S11}`:", ":math:`A=3.1944{10}^{-2}{m}^{2}` "," :math:`{I}_{z}=1.15{10}^{-5}{m}^{4}`"
    ":math:`\mathrm{S7}`:", ":math:`A=4.2130{10}^{-2}{m}^{2}` "," :math:`{I}_{z}=1.15{10}^{-5}{m}^{4}`"



* drivers


.. csv-table::

    ":math:`\mathrm{S4},\mathrm{S8}`:", "circular :math:`R=6.055{10}^{-2}m` "," :math:`e=6.2{10}^{-3}m` ", ""



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


.. csv-table::

    ":math:`\mathrm{M1}`:", ":math:`E=2.{10}^{11}\mathrm{Pa}` "," :math:`\rho =8000\mathrm{kg}/{m}^{3}` ", "(support frame)"
    ":math:`\mathrm{M2}`:", ":math:`E=5.{10}^{10}\mathrm{Pa}` "," :math:`\rho =2500\mathrm{kg}/{m}^{3}` ", "(insulating column)"
    ":math:`\mathrm{M3}`:", ":math:`E=7.{10}^{10}\mathrm{Pa}` "," :math:`\rho =2700\mathrm{kg}/{m}^{3}` ", "(aluminum connector and conductor)"


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

Points :math:`A`, :math:`E`, :math:`I`: embedding

Points :math:`D`, :math:`L`: non-continuity of :math:`{u}_{x}`, :math:`{\theta }_{y}`, :math:`{\theta }_{z}`

Laplace forces on drivers :math:`\mathrm{DH}`, :math:`\mathrm{HL}`;


* two-phase current :math:`\phi =\omega =100m`


* infinite conductors separated from :math:`1m`

:math:`I\mathrm{=}{I}_{\mathit{eff}}\sqrt{2}(\mathrm{cos}(\omega t+\phi )\mathrm{-}{e}^{\mathrm{-}t\mathrm{/}\tau }\mathrm{cos}\phi )`

:math:`{I}_{\mathrm{eff}}` effective current strength

:math:`\tau` time constant


* two short circuits with reclosing


.. csv-table::

    ":math:`t` "," :math:`0<t\le 0.135` "," :math:`0.135<t<0.580` "," :math:`0.580\le t\le 0.885`"
    "", "", "", ""
    ":math:`{I}_{\mathrm{eff}}` "," :math:`15.6\mathrm{kA}` "," :math:`0` "," :math:`15.6\mathrm{kA}`"
    "", "", "", ""
    ":math:`\tau` "," :math:`0.066s` ", ", "-", ":math:`0.062s`"



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

:math:`t=0`, zero speed and acceleration.