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


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

A modal calculation and harmonic response calculation are carried out on a basis composed of 10 natural modes.

To test the extraction and recovery of generalized quantities, a modification of the generalized terms is carried out in the Python environment, which consists in multiplying the generalized stiffness by two and in dividing the generalized second member vector by two.

The natural modes of the generalized model and the harmonic response to :math:`500\mathit{Hz}` are then calculated.

To calculate the harmonic response, a point excitation is applied to the coordinate point :math:`(0m\mathrm{,0}.1375m,0.03m)`.


.. image:: images/Object_4.png
    :width: 5.4756in
    :height: 2.6661in


.. _RefSchema_Object_4.png:

The results obtained are tested using diagonal storage and full storage successively with real matrices and complex matrices.


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

The mesh contains 240 elements of type HEXA8.


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

The first five natural frequencies of the generalized model and the displacement field are tested at the excitation frequency equal to :math:`500\mathit{Hz}` (without and with modification of the generalized terms).


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**"
    ":math:`{f}_{1}` (generalized quantities not modified)", "'SOURCE_EXTERNE'", "419.834215191 Hz"
    ":math:`{f}_{2}` (generalized quantities not modified)", "'SOURCE_EXTERNE'", "668.578057732 Hz"
    ":math:`{f}_{3}` (generalized quantities not modified)", "'SOURCE_EXTERNE'", "2485.22786476 Hz"
    ":math:`{f}_{4}` (generalized quantities not modified)", "'SOURCE_EXTERNE'", "2745.91955475 Hz"
    ":math:`{f}_{5}` (generalized quantities not modified)", "'SOURCE_EXTERNE'", "3626.81541778 Hz"
    ":math:`{f}_{1}` (modified generalized quantities)", "'SOURCE_EXTERNE'", "593.735241082 Hz"
    ":math:`{f}_{2}` (modified generalized quantities)", "'SOURCE_EXTERNE'", "945.51215675 Hz", "''"
    ":math:`{f}_{3}` (modified generalized quantities)", "'SOURCE_EXTERNE'", "3514.64295193 Hz"
    ":math:`{f}_{4}` (modified generalized quantities)", "'SOURCE_EXTERNE'", "3883.31667551 Hz"
    ":math:`{f}_{5}` (modified generalized quantities)", "'SOURCE_EXTERNE'", "5129.09155204 Hz", "''"
    "Harmonic response to :math:`500\mathit{Hz}`: sum of the components of the displacement field (generalized quantities not modified)", "'SOURCE_EXTERNE'", "-3.27788511305 10-5m"
    "Harmonic response to :math:`500\mathit{Hz}`: sum of the components of the displacement field (modified generalized quantities)", "'SOURCE_EXTERNE'", "1.18096814505 10-5m"