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


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

We model problem 1 with Euler's right beam elements: POU_D_E

**Problem 1:**


.. csv-table::

    "Mesh:", "beam :math:`\mathit{AC}`: 20 SEG2, 21 knots"
    "Boundary conditions:
    In all the knots
    in :math:`A`:
    in :math:`B`:
    in :math:`C`:", "DDL_IMPO =( TOUT =' OUI ', DZ=0.0, DRX =0.0, DRY =0.0,)
    (GROUP_NO ='A', DX=0.0, DY=0.0)
    (GROUP_NO ='B', DY=0.0,)
    (GROUP_NO ='C', DY=0.0,)"



notes
---------

The natural modes are calculated with a lock at point :math:`B` along the Y direction. A static mode is also calculated with a displacement imposed at point :math:`B` component :math:`\mathit{DY}`. The base of Ritz is composed of dynamic modes and static mode. It is orthogonalized with a generalized mode calculation and then returned to a mode_meca type concept.

The modal base is filtered to keep the first 5 modes.


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

**Frequencies (** :math:`\mathit{Hz}` **)**:


.. csv-table::

    "**Clean modes**", "**Reference** direct calculation", "**Aster**", "**tolerance**"
    "1", "5.6600453", "5.6600471", "0.1%"
    "2", "22.6403247", "22.6403247", "0.1%"
    "3", "50.9421205", "50.9433790", "0.1%"
    "4", "90.5703803", "90.5703803", "0.1%"
    "5", "141.5378176", "141.5651110", "0.1%"


**Effective masses and participation factors:**

For the effective masses and participation factors, the tests are based on the sum of the values for the first 5 modes.


.. csv-table::

    "**Parameter**", "**Reference** direct calculation", "**Aster**", "**tolerance**"
    "Sum of the effective masses for the first 5 modes", "342.9564379", "342.9564379", "0.1%"
    "Effective mass of the first mode", "297.9380528", "297.9380553", "0.1%"
    "Sum of the effective unit masses for the first 5 modes", "0.9330542", "0.9330463", "0.1%"
    "Sum of the absolute values of the participation factors for the first 5 modes", "26.4666220", "26.4660056", "0.1%"
    "Absolute value of the first mode participation factor", "17.2608821", "17.2608822", "0.1%"