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


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

The springs and point masses are modelled by discrete elements with 3 degrees of freedom DIS_T. Nodes :math:`N2` and :math:`N3` are slightly offset according to :math:`Y`, :math:`Y=\mathrm{0,01}m` and :math:`Y=-\mathrm{0,01}m` respectively, which does not change the results as only the problem according to :math:`X` is solved.


.. image:: images/100002010000017D000000D21A3CFE6296669D24.png
    :width: 2.7256in
    :height: 1.5028in


.. _RefImage_100002010000017D000000D21A3CFE6296669D24.png:

Node :math:`N1` is embedded and subjected to an imposed acceleration :math:`\gamma (t)`.

The mode of the first spring mass system is first calculated by imposing :math:`{u}_{x}({P}_{3})=0`. Then the mode of the second, by imposing :math:`{u}_{x}({P}_{2})=0`. A single modal base is created from these two modes, using the DEFI_BASE_MODALE command with the NUME_REF option. A dynamic calculation is then performed with the command DYNA_NON_LINE using modal damping deduced from these modes.


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

Number of knots: 3

Number of meshes and types: 2 DIS_T


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

The solutions tested are the relative displacement in :math:`t=10s`:


.. csv-table::

    "Node", "Reference", "Tolerance"
    ":math:`N2` (dot :math:`{P}_{2}`)", "0.538736"," 1%"
    ":math:`N3` (dot :math:`{P}_{3}`)", "0.538736"," 1%"