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


Calculation method
------------------

Here, we rely on a finite element model of the rectangular plate to build the reference solution. This modeling is based on square shell elements. The plate is discretized using :math:`20\mathrm{\times }40` elements.


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

We consider the first 5 natural frequencies of the supported plate:


* :math:`\mathrm{5,806}\mathit{Hz}`


* :math:`\mathrm{17,175}\mathit{Hz}`


* :math:`\mathrm{20,516}\mathit{Hz}`


* :math:`\mathrm{32,422}\mathit{Hz}`


* :math:`\mathrm{39,845}\mathit{Hz}`


Uncertainties about the solution
----------------------------

The proposed solution is slightly dependent on the choices of solvers made, and on the evolution of these solvers.