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


Calculation method used for the reference solution
--------------------------------------------------------

The reference solution is numerical: it is obtained with the software for calculating structures by finite elements SAMCEF.

The method for calculating natural frequencies is the method known as SORENSEN (algorithm by default in the CALC_MODES operator).


Benchmark results
----------------------

Since the structure has six rigid modes, we are interested in the first 10 non-zero natural frequencies.

The following table shows the values of the frequencies obtained (in :math:`\mathrm{Hz}`) according to the degree of the volume elements.


.. csv-table::

    "**Mode**", "**Degree 1**", "**Degree 2**"
    "1", "2.54231 E3", "2.47035 E3"
    "2", "2.54231 E3", "2.47035 E3"
    "3", "2.60747 E3", "2.47101 E3"
    "4", "2.60747 E3", "2.47101 E3"
    "5", "2.60747 E3", "2.47101 E3"
    "6", "2.74095 E3", "2.61296 E3"
    "7", "2.74095 E3", "2.61296 E3"
    "8", "2.74095 E3", "2.61430 E3"
    "9", "2.76313 E3", "2.61430 E3"
    "10", "2.76313 E3", "2.61430 E3"