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


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

**Discreet translational rigidity element**


.. image:: images/10000DF000001FF0000006349561F32E86807481.svg
    :width: 412
    :height: 80


.. _RefImage_10000DF000001FF0000006349561F32E86807481.svg:

Characteristics of the elements

.. csv-table::

    "DISCRET:", "with nodal masses", "M_T_D_N"
    "", "and stiffness matrices", "K_T_D_L"
    "", "and damping matrices", "A_T_D_L"


Boundary conditions:

.. csv-table::

    "in all nodes", "DDL_IMPO ", "(TOUT =' OUI 'DY= 0., DZ= 0.)"
    "at the end nodes", "", "(GROUP_NO =AB DX= 0.)"


Node names:

.. csv-table::

    ":math:`\mathrm{Point}A=\mathrm{N1}` "," :math:`{P}_{1}=\mathrm{N2}`"
    ":math:`\mathit{Point}B\mathrm{=}\mathit{N10}` "," :math:`{P}_{2}=\mathrm{N3}`"
    "", "..."
    "", ":math:`{P}_{8}=\mathrm{N9}`"



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

Number of knots: 10

Number of meshes and types: 9 SEG2


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

Real and imaginary parts of component :math:`\mathit{DX}` of the displacement of point :math:`{P}_{4}`.


.. csv-table::

    "**Frequency**", "**Reference**"
    "5.00", "1.0237E—4
    —8.5187E—6"
    "5.50", "4.5066E—4
    —7.7914E—4"
    "6.00", "—9.4101E—5
    —1.0585E—5"
    "10.00", "8.4143E—7
    —1.0335E—6"
    "15.00", "1.2656E—5
    —5.6652E—6"
    "20.00", "2.9784E—6
    —6.6970E—6"
    "25.00", "—1.2536E—6
    —5.2703E—6"
    "30.00", "—2.0904E—6
    —5.4821E—6"
    "35.00", "—4.5447E—6
    —1.1190E—6"
    "39.50", "—2.6895E—6
    —3.0505E—7"


Real and imaginary parts of the :math:`\mathrm{DX}` component of the speed of point :math:`{P}_{4}`.


.. csv-table::

    "**Frequency**", "**Reference**"
    "5.00", "2.6762E—4
    3.2160E—3"
    "5.50", "2.6925E—2
    1.5574E—2"
    "6.00", "3.9904E—4
    —3.5475E—3"
    "10.00", "6.4937E—5
    5.2869E—5"
    "15.00", "5.3393E—4
    1.1928E—3"
    "20.00", "8.4157E—4
    3.7428E—4"
    "25.00", "8.2786E—4
    —1.9691E—4"
    "30.00", "1.0333E—3
    —3.9403E—4"
    "35.00", "2.4608E—4
    —9.9943E—4"
    "39.50", "7.5709E—5
    —6.6749E—4"


Real and imaginary parts of the :math:`\mathit{DX}` component of the acceleration of point :math:`{P}_{4}`.


.. csv-table::

    "**Frequency**", "**Reference**"
    "5.00", "—1.0103E—1
    8.4076E—3"
    "5.50", "—5.3819E—1
    9.3047E—1"
    "6.00", "1.3374E—1
    1.5044E—2"
    "10.00", "—3.3218E—3
    4.0801E—3"
    "15.00", "—1.1242E—1
    5.0322E—2"
    "20.00", "—4.7033E—2
    1.0575E—1"
    "25.00", "3.0931E—2
    1.3004E—1"
    "30.00", "7.4273E—2
    1.9478E—1"
    "35.00", "2.1979E—1
    5.4116E—2"
    "39.50", "1.6566E—1
    1.8789E—2"



notes
---------

**Contents of the results file:**

The values of the displacement of component :math:`\mathrm{DX}` from point :math:`{P}_{4}` for all frequencies from :math:`5` to :math:`40\mathrm{Hz}` in steps of :math:`0.5` (Initial test case of VPCS).

The values of the speed and acceleration of the :math:`\mathrm{DX}` component of the point :math:`{P}_{4}` for some vibration frequencies.