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


Reference quantity and result
---------------------------------

We test the value of :math:`\mathrm{RMS}` in non-regression, on the total time of the normal force at the free end of the beam.

Two types of analyses were carried out:


* The first analysis to consist in calculating the transient dynamic response on a modal basis consisting of the first 30 natural modes.


* The second analysis consists in calculating the transient dynamic response on a modal basis consisting of 30 first natural modes to which static modes are added.

The calculation procedure is as follows:


* we calculate the first 30 natural frequencies (up to :math:`\mathrm{4800Hz}`) and the associated natural modes,


* the stiffness, mass and damping matrices are projected onto a modal basis,


* efforts are projected on a modal basis.


* the dynamic transient response is calculated on a modal basis


* we calculate RMS out of the total time of the normal force at node :math:`\mathrm{N2}`

We do not have a RMS reference value for this problem so we present the two results independently.


Reference quantity
---------------------


* RMS_T_TOTAL: value RMS based on the total normal force time (FORCE_NORMALE) at node :math:`\mathrm{N2}`.