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


Geometry
---------


.. image:: images/10001D86000069F00000249601740B32DE594656.svg
    :width: 620
    :height: 214


.. _RefImage_10001D86000069F00000249601740B32DE594656.svg:

     Beam length: :math:`l=10m`

     Mass :math:`B` is at a distance of :math:`\mathrm{0,5}m` from point :math:`A`.

     Beam cross section:

         Area: :math:`A=78.1{10}^{-4}{m}^{2}`

         Moments of inertia: :math:`{I}_{y}=5696.{10}^{-8}{m}^{4}`

                             :math:`{I}_{z}=2003.{10}^{-8}{m}^{4}`

                             :math:`{J}_{x}=7699.{10}^{-8}{m}^{4}`


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


.. csv-table::

    "Beam", "Young's module"
    density
    Poisson's ratio", ":math:`E={2.10}^{11}\mathrm{Pa}`
    :math:`\rho =0\mathrm{kg}/{m}^{3}`
    :math:`\nu =\mathrm{0,3}` ", "(zero beam mass)"
    "Mass in :math:`B` "," :math:`{m}_{B}=50000\mathrm{kg}` ", "", ""
    "Mass in :math:`C` "," :math:`{m}_{C}=5000\mathrm{kg}` ", "", ""



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

Point :math:`A` recessed.

Accelerated oscillator spectrum applied in :math:`A` in all three directions, with the same value for the 3 dampers :math:`\text{0,5\%}`, :math:`\text{1\%}` and :math:`\text{1,5\%}`.


.. image:: images/Object_1.svg
    :width: 620
    :height: 214


.. _RefImage_Object_1.svg:

For the calculation, a damping reduced by :math:`\text{1\%}` is used, with an interpolation (LOG LOG) in frequency and (LIN LOG) in damping.