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


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

For both problems, the reference solution is that obtained by a direct calculation of the natural modes. It is thus considered that the natural modes calculated by Code_Aster with a direct calculation are subject to validation by test case SDLL01 and correspond to the analytical solution. The effective masses and participation factors from this modal base are also used as a reference for validation.

Both problems are modelled with Euler's right beam elements: POU_D_E

**Problem 1:**


.. csv-table::

    "Cutting:", "beam :math:`\mathit{AC}`: 20 meshes SEG2"
    "Boundary conditions:
    In all the knots
    in :math:`A`:
    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 ='C', DY=0.0,)"


**Problem** 2 **:**


.. csv-table::

    "Cutting:", "beam :math:`\mathit{AC}`: 20 meshes SEG2"
    "Boundary conditions:
    in all nodes", "DDL_IMPO =( TOUT =' OUI ', DZ=0.0, DRX =0.0, DRY =0.0,)"



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

Frequencies, effective masses and participation factors of the first 5 natural modes obtained with a direct calculation.

For both problems, it is verified that the reference quantities are indeed identical to those obtained on a modal basis of the mode_meca type resulting from a concept of the mode_gene type.

For problem 2, we also check that for the three rigid body modes:

 - the sum of the effective masses corresponds to the mass of the beam,

 - the sum of the effective unit masses is equal to 1.