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


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

Beam element POU_D_T (Timoshenko's right beam)


.. image:: images/100008580000182F00000BE388AE8EB2C0A43423.svg
    :width: 312
    :height: 153


.. _RefImage_100008580000182F00000BE388AE8EB2C0A43423.svg:

Cutting: beam :math:`\mathrm{AB}`: 120 SEG2 meshes of variable cross section.


.. csv-table::

    "Boundary conditions:", ""
    "in all nodes", "" "DDL_IMPO (TOUT: 'OUI', DZ: 0., DRX: 0., DRY: 0.)""
    "at the knots", ""
    "extremities", "" (NOEUD: (AB) DX: 0., DY: 0., DRZ: 0.) """



.. csv-table::

    "Node names:", "Point :math:`A` "," :math:`x=0.` "," :math:`\mathrm{N1}`"
    "", "", ":math:`x=0.1` "," :math:`\mathrm{N21}`"
    "", "", ":math:`x=0.2` "," :math:`\mathrm{N41}`"
    "", "", ":math:`x=0.3` "," :math:`\mathrm{N61}`"
    "", "", ":math:`x=0.4` "," :math:`\mathrm{N81}`"
    "", "", ":math:`x=0.5` "," :math:`\mathrm{N101}`"
    "", "Point :math:`B` "," :math:`x=0.6` "," :math:`\mathrm{N121}`"



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


.. csv-table::

    "Number of nodes:", "121"
    "Number of meshes and types:", "120 SEG2"



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


.. csv-table::

    "**Clean mode order**", "**Frequency**
    **Reference**", "**% tolerance**"
    "1", "143.303", "1.6"
    "2", "396.821", "0.45"
    "3", "779.425", "0.3"
    "4", "1289.577", "0.9"


The natural modes of *Aster* have been normalized to 1. at the point of maximum translational amplitude as in the reference.

**Clean Mode** :math:`{F}_{i}(x)` **Normed to 1 at the maximum amplitude point**


.. csv-table::

    "", ":math:`i` "," :math:`x=0.1` "," :math:`x=0.2` "," "," :math:`x=0.3` "," :math:`x=0.4` "," :math:`x=0.5`"
    "Reference
    Aster
    % difference
    % tolerance", "1", "0.2349
    0.2363
    0.583
    0.6", "0.6962
    0.6970
    0.119
    0.15", "0.98960
    0.9895
    0.
    0.1", "0.8505
    0.8516
    0.132
    0.15", "0.3507
    0.3529
    0.631
    0.7"
    "Reference
    Aster
    % difference
    % tolerance", "2", "—0.4653
    —0.4670
    0.37
    0.4", "—0.7558
    —0.7555
    —0.041
    0.1", "0.
    —2.910—4
    —2.910—4
    1.10—3", "0.9232
    0.9226
    —0.063
    0.1", "0.6941
    0.6971
    0.435
    0.45"
    "Reference
    Aster
    % difference
    % tolerance", "3", "0.6278
    0.6290
    0.192
    0.2", "0.1969
    0.1952
    —0.89
    0.9", "—0.7783
    —0.7782
    —0.014
    0.1", "0.2406
    0.2377
    —1.226
    1.23", "0.9366
    0.9387
    0.228
    0.25"
    "Reference
    Aster
    % difference
    % tolerance", "4", "—0.666
    —0.6656
    —0.081
    0.1", "0.4832
    0.4840
    0.18
    0.2", "0.
    4.610—4
    4.610—4
    1.10—3", "—0.5901
    —0.5919
    0.31
    0.35", "0.9937
    0.9928
    —0.089
    0.1"



notes
---------

Calculations made by:


.. code-block:: text

    CALC_MODES
OPTION = 'PLUS_PETITE'
CALC_FREQ =_F (NMAX_FREQ = 4)
SOLVEUR_MODAL =_F (METHODE = 'TRI_DIAG')

**Contents of the results file:**

4 first natural frequencies, eigenvectors.