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


Geometry
---------

This is a problem originally proposed in the reference [:ref:`bib1 <bib1>`] and included in [:ref:`bib2 <bib2>`].


.. image:: images/10002198000069D500003D7F40D866C729DE86F7.svg
    :width: 475
    :height: 276


.. _RefImage_10002198000069D500003D7F40D866C729DE86F7.svg:


* beam :math:`\mathrm{AB}`: slender, massless beam with a length :math:`\mathrm{AB}`, :math:`l=\mathrm{10 }m` and a moment of inertia :math:`{I}_{Z}=\mathrm{0,3285}{m}^{4}`.


* point mass in :math:`B`: :math:`m=\mathrm{43,8}{10}^{\mathrm{3 }}\mathrm{kg}`


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


.. csv-table::

    "Young's module:", ":math:`E=4.{10}^{10}\mathrm{Pa}`"
    "Density:", ":math:`\rho =0\mathrm{kg}/{m}^{3}`"



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

**Boundary conditions:**

The only authorized movements are translations according to axis :math:`x`.

Point :math:`A` is embedded: :math:`\mathrm{dx}=\mathrm{dy}=\mathrm{dz}=\mathrm{drx}=\mathrm{dry}=\mathrm{drz}=0`.

**Loads:**


* modeling A: transverse acceleration at point A: :math:`\gamma (t)`


.. image:: images/1000096200002834000009B79EBACC0FC9A77866.svg
    :width: 475
    :height: 276


.. _RefImage_1000096200002834000009B79EBACC0FC9A77866.svg:


* B modeling: transverse force at point :math:`B`: :math:`\mathrm{Fx}(t)` with :math:`\mathrm{Fx}(t)=–\mathrm{m.}\gamma (t)`


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

The system is at rest: at :math:`t=0`, :math:`\mathrm{dx}(0)=0`, :math:`\mathrm{dx}/\mathrm{dt}(0)=0` at all points.