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


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


.. image:: images/Object_2.svg
    :width: 334
    :height: 485


.. _RefImage_Object_2.svg:


Characteristics of the mesh and the finite element model
--------------------------------------------------------

The mesh consists of 1860 nodes and 1800 quadrangular meshes on which shell DKT elements are assigned.


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

Natural frequencies :math:`(\mathit{Hz})`

Only frequencies and modes with an effective mass greater than :math:`\text{0.1\%}` are shown in the table below.


.. csv-table::

    "**Mode Number**", "**Ref**
    **(SAMCEF)**", "**Code_Aster**", "**Gap**", "**Gap** **between SAMCEF and** **Code_Aster** **in %**"
    "1 (47)", "2.80058", "2.80058", "2.80065", "0.003"
    "2 (48)", "2.80058", "2.80058", "2.80065", "0.003"
    "3 (158)", "5.92549", "5.92549", "5.92490", "-0.010"
    "4 (159)", "5.92549", "5.92549", "5.92490", "-0.010"


These four modes make it possible to obtain a good representation of the mass in the direction of excitation since the cumulative effective masses in the directions :math:`x` and :math:`y` amount to :math:`\text{83.2\%}`.

Horizontal displacement :math:`x(m)`:


+------------+----------------------+---------+--------------+----------+----------------+-------+
|**Altitude**|**CA** AND **EM 2000**          |**Aster_code**           |**Variance (%)**        |
+------------+----------------------+---------+--------------+----------+----------------+-------+
|            |CQC                   |SRSS     |CQC           |SRSS      |CQC             |SRSS   |
+------------+----------------------+---------+--------------+----------+----------------+-------+
|13.3        |1.318E-03             |1.316E-03|1.538 E-03    |1.432 E-03|16.653          |8.740  |
+------------+----------------------+---------+--------------+----------+----------------+-------+
|26.8        |1.484E-03             |1.485E-03|2.853 E-03    |2.669 E-03|92.155          |79.744 |
+------------+----------------------+---------+--------------+----------+----------------+-------+
|40.3        |1.898E-03             |1.898E-03|4.456 E-03    |4.249 E-03|134.714         |123.819|
+------------+----------------------+---------+--------------+----------+----------------+-------+
|49.4        |2.4448E-03            |2.442E-03|5.693 E-03    |5.495 E-03|132.872         |124.948|
+------------+----------------------+---------+--------------+----------+----------------+-------+
|63.08       |3.278E-03             |3.275E-03|7.822 E-03    |7.657 E-03|138.603         |133.751|
+------------+----------------------+---------+--------------+----------+----------------+-------+
|76.8        |4.570E-03             |4.568E-03|1.026 E-02    |1.014 E-02|124.510         |121.860|
+------------+----------------------+---------+--------------+----------+----------------+-------+
|90.7        |5.918E-03             |5.918E-03|1.293 E-02    |1.283 E-02|118.516         |116.802|
+------------+----------------------+---------+--------------+----------+----------------+-------+
|100         |7.023E-03             |7.024E-03|1.477 E-02    |1.467 E-02|110.294         |108.862|
+------------+----------------------+---------+--------------+----------+----------------+-------+
|109.3       |7.677E-03             |7.677E-03|1.658 E-02    |1.648 E-02|115.998         |114.614|
+------------+----------------------+---------+--------------+----------+----------------+-------+
|127.9       |9.053E-03             |9.054E-03|1.990 E-02    |1.975 E-02|119.818         |118.117|
+------------+----------------------+---------+--------------+----------+----------------+-------+

Vertical displacement :math:`z(m)`:


+------------+---------------+---------+--------------+----------+----------------+-------+
|**Altitude**|**CASTEM 2000**          |**Aster_code**           |**Variance (%)**        |
+------------+---------------+---------+--------------+----------+----------------+-------+
|            |CQC            |SRSS     |CQC           |SRSS      |CQC             |SRSS   |
+------------+---------------+---------+--------------+----------+----------------+-------+
|13.3        |4.534E-04      |4.540E-04|8.297 E-04    |8.101 E-04|82.955          |78.407 |
+------------+---------------+---------+--------------+----------+----------------+-------+
|26.8        |6.832E-04      |6.832E-04|1.712 E-03    |1.674 E-03|150.528         |145.025|
+------------+---------------+---------+--------------+----------+----------------+-------+
|40.3        |1.091E-03      |1.091E-03|2.464 E-03    |2.408 E-03|125.872         |120.680|
+------------+---------------+---------+--------------+----------+----------------+-------+
|49.4        |1.510E-03      |1.510E-03|2.892 E-03    |2.823 E-03|91.521          |86.877 |
+------------+---------------+---------+--------------+----------+----------------+-------+
|63.08       |1.794E-03      |1.795E-03|3.424 E-03    |3.337 E-03|90.769          |85.848 |
+------------+---------------+---------+--------------+----------+----------------+-------+
|76.8        |1.944E-03      |1.945E-03|3.840 E-03    |3.737 E-03|97.437          |92.035 |
+------------+---------------+---------+--------------+----------+----------------+-------+
|90.7        |2.024E-03      |2.025E-03|4.173 E-03    |4.056 E-03|106.143         |100.213|
+------------+---------------+---------+--------------+----------+----------------+-------+
|100         |2.114E-03      |2.115E-03|4.372 E-03    |4.244 E-03|106.767         |100.630|
+------------+---------------+---------+--------------+----------+----------------+-------+
|109.3       |2.187E-03      |2.188E-03|4.564 E-03    |4.427 E-03|108.645         |102.266|
+------------+---------------+---------+--------------+----------+----------------+-------+
|127.9       |2.356E-03      |2.358E-03|4.959 E-03    |4.803 E-03|110.427         |103.663|
+------------+---------------+---------+--------------+----------+----------------+-------+


notes
---------

The calculation is carried out without taking into account the neglected modes. In direction :math:`Z`, a single mode, No. 196, with a frequency lower than :math:`7\mathit{Hz}`, has an effective mass greater than :math:`0.1\text{\%}`