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


Geometry
---------


.. image:: images/10000B200000249600000E43C10B541F7D82344B.svg
    :width: 471
    :height: 183


.. _RefImage_10000B200000249600000E43C10B541F7D82344B.svg:


.. csv-table::

    "Length: :math:`L\mathrm{=}10` "," :math:`(a\mathrm{=}\stackrel{ˉ}{\mathit{AD}}b\mathrm{=}\stackrel{ˉ}{\mathit{DB}})` "," :math:`\begin{array}{c}{m}_{e}\mathrm{=}\mathit{lmabda}\rho AL\mathrm{=}780\lambda \mathit{kg}\\ {k}_{e}\mathrm{=}{\pi }^{4}{m}_{e}\mathrm{=}780\lambda {\pi }^{4}N\mathrm{/}m\end{array}`"


Straight section:


.. csv-table::

    "air", ":math:`A\mathrm{=}{1.10}^{\mathrm{-}2}{m}^{2}`"
    "moment of inertia", ":math:`\mathit{Iz}\mathrm{=}3.9{10}^{\mathrm{-}6}{m}^{4}`"


**3 cases to study:**

:math:`\lambda =0.`

:math:`\lambda =0.001`

:math:`\lambda =0.01`

Point coordinates (meters):


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," :math:`D`"
    ":math:`x` ", "0. ", "10. ", "2.5", "2.5"
    ":math:`y` ", "0. ", "0. "," :math:`\mathit{qcq}\mathrm{\ne }0` ", "0."



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

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

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


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


.. csv-table::

    "Point :math:`A`:", ":math:`u=v=0.`"
    "Point :math:`B`:", ":math:`v=0.`"
    "Point :math:`C`:", ":math:`u=0.` :math:`\theta =0.` vertical slide"



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

Not applicable for modal analysis.