Benchmark solution
=====================


Baseline calculations
--------------------

No benchmark results. Frequencies and displacements are tested by non-regression.


Reference quantities and results
-----------------------------------


* :math:`\mathrm{FREQ}`: frequency


* :math:`\mathrm{DZ}`: next move :math:`z`

Achieved results:


* From a modal base defined from the assembly of two dynamic mode bases.


+---------------------+-----------+-------------------------------+
|Component            |Fashion no.|Reference :math:`(\mathrm{Hz})`|
+---------------------+-----------+-------------------------------+
|:math:`\mathrm{FREQ}`|:math:`1`  |:math:`29.0604`                |
+                     +-----------+-------------------------------+
|                     |:math:`2`  |:math:`76.2281`                |
+                     +-----------+-------------------------------+
|                     |:math:`3`  |:math:`76.2281`                |
+                     +-----------+-------------------------------+
|                     |:math:`4`  |:math:`76.2281`                |
+                     +-----------+-------------------------------+
|                     |:math:`5`  |:math:`5058.51`                |
+                     +-----------+-------------------------------+
|                     |:math:`6`  |:math:`5058.51`                |
+---------------------+-----------+-------------------------------+


* From a modal base defined from static modes


.. csv-table::

    "Component", ":math:`N°` mode", "Reference :math:`(\mathrm{Hz})`"
    ":math:`\mathrm{FREQ}` "," :math:`1` "," :math:`4.9762`"



* Based on a harmonic calculation carried out on the modal basis of static modes.


+-------------------+--------------+---------+--------------------------------+
|Component                         |Point    |Reference :math:`(m)`           |
+-------------------+--------------+---------+--------------------------------+
|:math:`\mathrm{DZ}`|Real part     |:math:`E`|:math:`2.02777\times {10}^{-6}` |
+                   +--------------+         +--------------------------------+
|                   |Imaginary part|         |:math:`-5.38827\times {10}^{-5}`|
+-------------------+--------------+---------+--------------------------------+