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


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

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

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

Boundary conditions:

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


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

Number of knots: 2

Number of meshes and types: 1 SEG2, 2 POI1


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

**Random dynamic response**


.. csv-table::

    "**Identification**", "**Reference**"
    "ABSOLU: :math:`F\mathrm{=}5.\mathit{Hz}` ", "1.2307"
    "ABSOLU: :math:`F\mathrm{=}10.\mathit{Hz}` ", "2.7116"
    "ABSOLU: :math:`F\mathrm{=}15.\mathit{Hz}` ", "47.2154"
    "ABSOLU: :math:`F\mathrm{=}20.\mathit{Hz}` ", "2.8924"
    "ABSOLU: :math:`F\mathrm{=}25.\mathit{Hz}` ", "0.47047"
    "RELATIF: :math:`F\mathrm{=}5.\mathit{Hz}` ", "0.01197"
    "RELATIF: :math:`F\mathrm{=}10.\mathit{Hz}` ", "0.04209"
    "RELATIF: :math:`F\mathrm{=}15.\mathit{Hz}` ", "36.9225"
    "RELATIF: :math:`F\mathrm{=}20.\mathit{Hz}` ", "7.1006"
    "RELATIF: :math:`F\mathrm{=}25.\mathit{Hz}` ", "2.7953"
    "DIFFERENTIEL: :math:`F\mathrm{=}5.\mathit{Hz}` ", "1.0"
    "DIFFERENTIEL: :math:`F\mathrm{=}10.\mathit{Hz}` ", "1.0"
    "DIFFERENTIEL: :math:`F\mathrm{=}15.\mathit{Hz}` ", "1.0"
    "DIFFERENTIEL: :math:`F\mathrm{=}20.\mathit{Hz}` ", "1.0"
    "DIFFERENTIEL: :math:`F\mathrm{=}25.\mathit{Hz}` ", "1.0"


**Post-treatment on the absolute displacement response: spectral moments and statistical parameters**


.. csv-table::

    "**Identification**", "**Reference**", "**% Tolerance**"
    "Spectral moment no. 0", "505.70832"," 0.1%"
    "Spectral moment No. 1, "49047.8 104"," 0.1%"
    "Spectral moment No. 2", "5.025066 106"," 0.1%"
    "Spectral moment No. 3", "5.52943 108"," 0.1%"
    "Spectral moment no. 4", "7.2059956 1010"," 0.1%"
    "Standard deviation", "22.49"," 0.1%"
    "Irregularity factor", "0.8324"," 0.1%"
    "Apparent frequency (:math:`\mathrm{Hz}`)", "15.86"," 0.1%"
    "Average number of zeros per second", "31.73"," 0.1%"
    "Spectral moment No. 6", "4.186992 1015"," 0.1%"
    "Spectral moment No. 7, "1.7826555 1018"," 0.1%"
    "Spectral moment No. 10, "2.468734 1026"," 0.1%"