Reference problem
=====================


.. image:: images/10000000000002B3000003339A7B7FE4DC6DFBF8.png
    :width: 3.1311in
    :height: 4.3217in


.. _RefImage_10000000000002B3000003339A7B7FE4DC6DFBF8.png:


Geometry
---------

Cylinder height :math:`H\mathrm{=}10m`

Inner cylinder radius :math:`{R}_{1}\mathrm{=}0.5m`

fluid thickness :math:`e\mathrm{=}1m` (External cylinder radius :math:`{R}_{2}\mathrm{=}2m`)

plate thickness :math:`h=0.5m`


Material properties
------------------------

Structure: :math:`{\rho }_{s}\mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}`, :math:`E\mathrm{=}2.1{10}^{11}\mathit{Pa}`, :math:`\nu \mathrm{=}0.3` (steel).


Boundary conditions and loads
-------------------------------------

Structure:


* the cylinder is subject to balancing around a pivot located upstream of the axial annular flow along this cylinder:

:math:`{X}_{1}\mathrm{=}z`

     Parameter for spectrum calculation:


* Cutoff frequency: :math:`F\mathrm{=}\mathrm{15Hz}`


* Constant for the magnitude of the pressure spectrum :math:`K\mathrm{=}\mathrm{3,4}{e}^{\mathrm{-}5}{s}^{1\mathrm{/}2}\mathrm{/}{m}^{3\mathrm{/}2}`


* Hydraulic diameter for the amplitude of the pressure spectrum :math:`d\mathrm{=}\mathrm{1,5}`


* Coefficient of the convective speed of vortices in the axial direction (direction of flow) :math:`\alpha \mathrm{=}\mathrm{0,65}`


* The correlation lengths for turbulence in the axial and orthoradial directions are equal to :math:`\lambda \mathrm{=} \lambda\text{'} \mathrm{=} \mathrm{5}`