Modeling A
==============


Characteristics of modeling
------------------------

The mass-spring system is modelled by a discrete element DIS_T.


.. image:: images/100005840000064E00000AA5B1C8DC96F216C0DC.svg
    :width: 81
    :height: 137


.. _RefImage_100005840000064E00000AA5B1C8DC96F216C0DC.svg:

Numeric data:


.. csv-table::

    "for the mass-spring system:", ":math:`m=\mathrm{450 }\mathrm{kg}`"
    "for the floor:", ":math:`{k}_{\mathrm{0 }}={10}^{\mathrm{5 }}N/m`"
    "for non-linearity:", ":math:`{x}_{\mathrm{0 }}=\mathrm{0,1 }m`; :math:`a=\mathrm{0,01}` and :math:`\omega =\pi /4`."


The time integration is carried out with the Euler algorithm or the Devogelaere algorithm and a time step of 0.02 seconds. The calculations are archived every time step.

We consider reduced damping :math:`{\xi }_{i}` to zero for all the calculated modes.


Characteristics of the mesh
----------------------------

The mesh consists of a node and a POI1 type mesh.


Tested sizes and results
------------------------------

We check the natural frequency of the oscillator as well as the relative movements of the node :math:`\mathrm{NO1}` at different times (for the integration algorithm EULER).


.. csv-table::

    "**Frequency (Hz)**", "**Reference**"
    "", "2.37254"


Relative displacement of node :math:`\mathrm{NO1}` with the Euler numerical integration algorithm:


.. csv-table::

    "**Time (s)**", "**Reference**"
    "2", "0.01"
    "6", "—0.01"
    "10", "0.01"
    "14", "—0.01"
    "18", "0.01"


Relative displacement of node :math:`\mathrm{NO1}` with Devogelaere's numerical integration algorithm:


.. csv-table::

    "**Time (s)**", "**Reference**"
    "2", "0.01"
    "6", "—0.01"
    "10", "0.01"
    "14", "—0.01"
    "18", "0.01"