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


Reference calculation
-------------------

Outline of the test case:


* Calculation of the natural modes of each triangle


    * :math:`\mathrm{TRI1}` AND :math:`\mathrm{TRI2}`, look for clean modes for :math:`f\in [\mathrm{10,3000}]`


    * :math:`\mathrm{TRI3}` AND :math:`\mathrm{TRI4}`, search for the first :math:`25` clean modes


* Definition and calculation of the static modal base of each triangle


* Creation of a static generalized model by coupling the bases


* Calculation and retrieval, on a physical basis, of the modes of the global structure


    * Travel test


    * Natural frequency test


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


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


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

Testing the results returned on a physical basis:


.. csv-table::

    "", "Component", "Reference :math:`(m)`"
    "Move node :math:`\mathrm{NO1}` "," :math:`\mathrm{DZ}` "," :math:`0.454388`"
    "Move node :math:`\mathrm{NO43}` "," :math:`\mathrm{DZ}` "," :math:`0.60375`"


Test of natural frequency values:


+---------+-----------+-------------------------------+
|Component|Fashion no.|Reference :math:`(\mathrm{Hz})`|
+---------+-----------+-------------------------------+
|FREQ     |:math:`1`  |:math:`5.5`                    |
+         +-----------+-------------------------------+
|         |:math:`2`  |:math:`21.66`                  |
+         +-----------+-------------------------------+
|         |:math:`3`  |:math:`23.64`                  |
+         +-----------+-------------------------------+
|         |:math:`4`  |:math:`55.63`                  |
+         +-----------+-------------------------------+
|         |:math:`5`  |:math:`56.97`                  |
+---------+-----------+-------------------------------+