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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 560
    :height: 279


.. _RefImage_Object_1.svg:


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

:math:`E\mathrm{=}98\mathrm{696,044}\mathit{MPa}`

:math:`\nu \mathrm{=}0`

:math:`\rho \mathrm{=}{3.10}^{6}\mathit{kg}\mathrm{/}{m}^{3}`

Rayleigh proportional damping: :math:`C\mathrm{=}\lambda K+\mu M`, :math:`\lambda \mathrm{=}5.{10}^{\mathrm{-}4}`, :math:`\mu \mathrm{=}5`


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

Imposed displacement at the end :math:`C`: :math:`u(C)\mathrm{=}\stackrel{ˉ}{u}f(t)` with :math:`\stackrel{ˉ}{u}\mathrm{=}{10}^{\mathrm{-}3}m` and :math:`f(t)` evolution as a function of Heaviside time: :math:`f(t)\mathrm{=}1`, :math:`t\mathrm{\ge }0`.

:math:`A` recessed end


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

Zero initial displacement at all points.

Initial speed zero at all points.