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


Geometry
---------


.. image:: images/100000000000020D0000015ACB61678B1A4BAA28.png
    :width: 3.7465in
    :height: 2.2626in


.. _RefImage_100000000000020D0000015ACB61678B1A4BAA28.png:

:math:`L=0.69215m`

:math:`l=0.43815m`

:math:`H=0.473075m`

Hollow circular section:

:math:`{d}_{e}=0.060m`

:math:`{d}_{i}=0.052m`

:math:`S=0.7037{10}^{-3}{m}^{2}`

:math:`{I}_{y}={I}_{z}=0.2772{10}^{-6}{m}^{4}`

:math:`{A}_{y}={A}_{z}=2.`

:math:`{C}_{y}=0.5545{10}^{-6}{m}^{4}`


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

:math:`E=1.92276\mathrm{E11}N/{m}^{2}`

:math:`\nu =0.3`

:math:`\rho =7800.0\mathrm{kg}/{m}^{3}`

     Four masses of :math:`4.444\mathrm{kg}` are located at the four upper vertices, see figure.


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


* Structure embedded at its base,


* Modal amortizations from :math:`\text{2 \%}`.

Definition of the acceleration spectrum at the supports


.. csv-table::

    "Frequency", ":math:`X` :math:`Z` "," :math:`Y`"
    "100", "17.3", "11.5"
    "110", "16.3", "10.9"
    "120", "15.3", "10.2"
    "130", "14.3", "9.6"
    "300", "10.2", "6.66"



* for an amortization of :math:`\text{2 \%}`,


* acceleration in :math:`g`.