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


Geometry
---------

We consider the system represented by the diagram below:


.. image:: images/100000000000028000000180A97838A70A6D00BD.png
    :width: 4.5256in
    :height: 2.6075in


.. _RefImage_100000000000028000000180A97838A70A6D00BD.png:


.. csv-table::

    "Point masses:", ":math:`{m}_{1}` and :math:`{m}_{2}`"
    "Link stiffness:", ":math:`{k}_{1}` and :math:`{k}_{2}`"
    "Hysteretic damping:", ":math:`{\eta }_{1}` and :math:`{\eta }_{2}`"



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


.. csv-table::

    "Linear elastic translation spring", ":math:`{K}_{1}\mathrm{=}28000N\mathrm{/}m`"
    "", ":math:`{K}_{2}\mathrm{=}28000N\mathrm{/}m`"
    "Point mass", ":math:`{M}_{1}\mathrm{=}10\mathit{kg}`"
    "", ":math:`{M}_{2}\mathrm{=}5\mathit{kg}`"
    "Hysteretic damping", ":math:`{\eta }_{1}\mathrm{=}0.1`"
    "", ":math:`{\eta }_{2}\mathrm{=}0.0`"



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

Boundary conditions:

Points :math:`A`, :math:`B`, :math:`C` embedded in :math:`\mathit{DY}` and :math:`\mathit{DZ}`

Points :math:`A`: recessed :math:`(\mathit{DX}\mathrm{=}0)`.

Loading: Sinusoidal concentrated force with variable frequency at point :math:`C`

:math:`\begin{array}{c}{F}_{{x}_{4}}\mathrm{=}{F}_{0}\mathrm{sin}\Omega t\\ \Omega \mathrm{=}2\pi f0\mathit{Hz}\mathrm{\le }f\mathrm{\le }21.0543\mathit{Hz}\\ {F}_{0}\mathrm{=}\mathit{constante}\mathrm{=}\mathrm{100N}\end{array}`


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

Not applicable to the study of the permanent harmonic regime.