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


Geometry
---------


.. image:: images/10000D8600002CA6000012EAFAFED834F440FB5E.svg
    :width: 576
    :height: 244


.. _RefImage_10000D8600002CA6000012EAFAFED834F440FB5E.svg:

:math:`L=1m`

:math:`D=\mathrm{0,2}m` - Circular section


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

:math:`E={1.10}^{10}\mathrm{Pa}`

:math:`\nu =0.3`

:math:`\rho ={1.10}^{4}\mathrm{kg}/{m}^{3}`

Rayleigh damping by element: :math:`{\alpha }_{e}=0.1` :math:`{\beta }_{e}=0.1`


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

Enclosed end :math:`A`: :math:`u(0)=n(0)=w(0)=0`.

For any point :math:`M(x)`: :math:`n(0)=w(0)=0`.

Harmonic loading over time, at the free end:


* orientation: according to :math:`x`,


* amplitude: :math:`\mathrm{100 }N`,


* frequency: :math:`\mathrm{100 }\mathrm{Hz}`.


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

Not applicable for harmonic response calculation.