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


Geometry
---------


.. image:: images/10000848000021B1000010A43B723D343AAF0CE7.svg
    :width: 434
    :height: 214


.. _RefImage_10000848000021B1000010A43B723D343AAF0CE7.svg:


.. csv-table::

    "Square section beam:", ":math:`c=0.014m`"
    ":math:`L`: length of the beam", ":math:`L=0.783m`"
    "Strain gauge", ":math:`x=0.462m`"



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


.. csv-table::

    "Young's module:", ":math:`E=6.7E10\mathrm{Pa}`"
    "Density:", ":math:`\rho =2400\mathrm{kg}/{m}^{3}`"
    "Poisson's ratio:", ":math:`\nu =0.`"



.. csv-table::

    "Spring stiffness:", "case no. 1 :math:`k=18000N/m` ", "case no. 2 :math:`k=45\mathrm{000N}/m`"



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


.. csv-table::

    "At point :math:`A`:", ":math:`u=v=0` (ball joint)"
    "At point :math:`B`:", "free end before impact (:math:`t<0`)"


**Charging:**

No other load.

The effects of gravity are negligible at first approximation.


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

For :math:`t<0` at any point on the abscissa :math:`x`


* :math:`\mathrm{dv}/\mathrm{dt}=\omega \mathrm{.}x`


* :math:`\omega =–3.8\mathrm{rd}/s`

For :math:`t=0`, :math:`v(L\mathrm{,0})=0`: contact of the free end with the spring.