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


Geometry
---------


.. image:: images/100011200000298C0000094D11B1F3F93BC4BD8E.svg
    :width: 536
    :height: 120


.. _RefImage_100011200000298C0000094D11B1F3F93BC4BD8E.svg:


.. csv-table::

    "Point masses:", ":math:`{m}_{{P}_{1}}={m}_{{P}_{2}}={m}_{{P}_{3}}=\dots \dots ={m}_{{P}_{8}}=m`"
    "Link stiffness:", ":math:`{k}_{\mathrm{AP1}}={k}_{\mathrm{P1P2}}={k}_{\mathrm{P2P3}}=\dots \dots ={k}_{\mathrm{P8B}}=k`"
    "Viscous damping:", ":math:`{c}_{\mathrm{AP1}}={c}_{\mathrm{P1P2}}={c}_{\mathrm{P2P3}}=\dots \dots ={c}_{\mathrm{P8B}}=c`"



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


.. csv-table::

    "Linear elastic translation spring", ":math:`k={10}^{5}N/m`"
    "Point mass", ":math:`m=10\mathrm{Kg}`"
    "Unidirectional viscous damping", ":math:`c=50N/(m/s)`"



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

Boundary conditions:

Points :math:`A` and :math:`B`: recessed :math:`(u=0)`.

Loading: Sinusoidal concentrated force with variable frequency at point :math:`{P}_{4}`


.. csv-table::

    "Point :math:`{P}_{4}` "," :math:`{F}_{{x}_{4}}\mathrm{=}{F}_{0}\mathrm{sin}\Omega t` "," :math:`\Omega \mathrm{=}2\pi f` :math:`5\mathrm{Hz}\le f\le 40\mathrm{Hz}`"
    "", "", ":math:`{F}_{0}\mathrm{=}\mathit{constante}\mathrm{=}\mathrm{1N}`"
    "Other points :math:`{P}_{i}` "," :math:`{f}_{{x}_{i}}=0` ", ""



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

Not applicable to the study of the permanent harmonic regime.