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


Geometry
---------


.. image:: images/100016B20000165300000C3284D2CC84EAAE1335.svg
    :width: 288
    :height: 157


.. _RefImage_100016B20000165300000C3284D2CC84EAAE1335.svg:

**Point coordinates (in** :math:`m` **) :**


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C`"
    ":math:`x` ", "0. ", "10. ", "10."
    ":math:`y` ", "0. ", "0. "," :math:`\mathit{yc}`"
    ":math:`z` ", "0. ", "0. ", "0."


length of the beam: :math:`\mathit{AB}\mathrm{=}L\mathrm{=}10m`

Point mass in :math:`C`: :math:`{m}_{c}\mathrm{=}1000\mathit{kg}`

**Tubular section:**


.. csv-table::

    "outside diameter", ":math:`\mathrm{de}=0.350m`"
    "inner diameter", ":math:`\mathit{di}\mathrm{=}0.320m`"
    "air", ":math:`A\mathrm{=}1.57865{10}^{\mathrm{-}2}{m}^{2}`"
    "inertia", ":math:`\mathrm{Iy}=\mathrm{Iz}=2.21899{10}^{-4}{m}^{4}`"
    "polar inertia", ":math:`\mathit{Ip}\mathrm{=}4.43798{10}^{\mathrm{-}4}{m}^{4}`"



.. csv-table::

    "**2 cases studied:**", "1) :math:`\mathrm{yc}=0.`"
    "", "2) :math:`\mathit{yc}\mathrm{=}1.m`"



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

:math:`E\mathrm{=}2.1{10}^{11}\mathit{Pa}`

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


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

Embedded point :math:`A`: (:math:`u\mathrm{=}v\mathrm{=}w\mathrm{=}0`, :math:`{\theta }_{x}\mathrm{=}{\theta }_{y}\mathrm{=}{\theta }_{z}\mathrm{=}0`).


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

Not applicable for modal analysis.