B modeling
==============

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

     Model A is repeated, but by adding damping to the mass/spring system.

**Discreet element in type translation** **DIS_T**


.. image:: images/10000262000010F30000048C5BF6BDB2083723BD.svg
    :width: 218
    :height: 58


.. _RefImage_10000262000010F30000048C5BF6BDB2083723BD.svg:

Characteristics of the elements:

At nodes :math:`\mathrm{P1}` and :math:`\mathrm{P2}`: mass matrices of type M_T_D_N with :math:`m=100\mathrm{kg}`.

Between :math:`\mathrm{P1}` and :math:`\mathrm{P2}`: a K_T_D_L stiffness matrix with :math:`{K}_{x}={10}^{6}N/m`

Boundary conditions:

All degrees of freedom are locked except degree of freedom :math:`\mathrm{DX}` from node :math:`\mathrm{P2}`.



Damping: A :math:`\mathrm{0,1}\text{}` reduction in damping is added to the system.

It is introduced into the test case, either usually by the keyword AMOR_REDUIT, or, to validate the functionality RELA_EFFO_VITE, by a linear relationship between the mass/spring speed and a force applied to the node :math:`\mathrm{P2}`.


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

Number of knots: 2

Number of meshes and types: 1 SEG2, 2 POI1


Features tested
-----------------------

In particular, in this modeling, the functionality RELA_EFFO_VITE of the DYNA_VIBRA operator (BASE_CALCUL =' GENE ') is tested in this modeling. Through its use, it is possible to introduce a non-linear behavior dependent on the speed of a point. Here we validate this relationship in a simple way in the linear case by comparing it with a modal damping behavior (which, in the case of a single mode, amounts to viscous damping).


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


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    "DYNA_VIBRA (BASE_CALCUL =' GENE ') AMOR_REDUIT "," :math:`\mathrm{0,53}\text{m}` ", "1%"
    "DYNA_VIBRA (BASE_CALCUL =' GENE ') RELA_EFFO_VITE "," :math:`\mathrm{0,53}\text{m}` ", "1%"
    "DYNA_VIBRA (BASE_CALCUL =' GENE ') AMOR_REDUIT "," :math:`0.531338` (non regression)", "1.E -4%"
    "DYNA_VIBRA (BASE_CALCUL =' GENE ') RELA_EFFO_VITE "," :math:`0.531338` (non regression)", "1.E -4%"