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


Geometry
---------


.. image:: images/10000D520000323B00000C18D8774116216CD7DC.svg
    :width: 648
    :height: 156


.. _RefImage_10000D520000323B00000C18D8774116216CD7DC.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{P1P2}}={c}_{\mathrm{P2P3}}=\dots \dots ={C}_{\mathrm{P7P8}}=c`
    :math:`{C}_{\mathrm{AP1}}=\mathrm{cc}`
    :math:`{C}_{\mathrm{P8B}}=\mathrm{cd}`"



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


.. csv-table::

    "Linear elastic translation spring", ":math:`k={10}^{5}N/m`"
    "Point mass", ":math:`m=10\mathrm{kg}`"
    "Link damping", ":math:`c=50N/(m/s)`"
    "", ":math:`\mathrm{cc}=250N/(m/s)`"
    "", ":math:`\mathrm{cd}=25N/(m/s)`"



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

Embedded :math:`A` and :math:`B` points: :math:`u=0`

**Loading:** Non-periodic concentrated force at point :math:`\mathrm{P4}`


+-------------------------------------------------------------------------------------------------------------------+-------------------------+------------------------------------------------------------------------------------+-------------------------------------------------------------------------+
|                                                                                                                   |Point :math:`\mathrm{P4}`|:math:`{F}_{{x}_{4}}=F(t)0\le t\le \mathrm{1s}`                                     |:math:`F(t)=\mathrm{1N}=\mathrm{constante}`                              |
+ .. image:: images/100002F000000BE3000009182C742061EEE9F1DE.svg                                                    +                         +                                                                                    +                                                                         +
|    :width: 648                                                                                                    |                         | :math:`t>\mathrm{1s}`                                                              | :math:`F(t)=0`                                                          |
+    :height: 156                                                                                                   +                         +                                                                                    +                                                                         +
|                                                                                                                   |                         |                                                                                    |                                                                         |
+                                                                                                                   +                         +                                                                                    +                                                                         +
|                                                                                                                   |                         |                                                                                    |                                                                         |
+-------------------------------------------------------------------------------------------------------------------+-------------------------+------------------------------------------------------------------------------------+-------------------------------------------------------------------------+



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

For :math:`t=0`, in every way :math:`{P}_{i}`: :math:`u=0`, :math:`\frac{\mathrm{du}}{\mathrm{dt}}=0`.