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


Geometry
---------

The pipe is a hollow cylinder with a circular cross section, filled with fluid.


.. image:: images/1000000000000CE4000004FED5AF347B66D05F9F.png
    :width: 5.5in
    :height: 2.1299in


.. _RefImage_1000000000000CE4000004FED5AF347B66D05F9F.png:

Characteristics of the pipe:


.. csv-table::

    "length:", ":math:`L=\mathrm{1,0}m`"
    "outside diameter:", ":math:`D=\mathrm{0,1}m`"
    "thickness:", ":math:`\mathrm{ep}=\mathrm{0,01}m`"


For modeling C, the section is modified, which becomes variable: the diameter varies from 0.1 to 0.11 m while the thickness varies from 0.011 to 0.01 m.


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

The physical characteristics of the material constituting the tube are as follows:

Young's modulus: :math:`E=\mathrm{1,0}·{10}^{10}\mathrm{Pa}`

Poisson's ratio: :math:`\nu =\mathrm{0,3}`

density: :math:`{\rho }_{s}=\mathrm{1,0}·{10}^{4}\mathrm{kg}/{m}^{3}`

Longitudinal wave speed: :math:`{c}_{s}=\sqrt{\frac{E}{{\rho }_{s}}}=\mathrm{1,0}·{10}^{3}m/s`

The physical characteristics of the fluid material in the tube are as follows:

density: :math:`{\rho }_{f}=\mathrm{1,0}·{10}^{3}\mathrm{kg}/{m}^{3}`

speed of sound: :math:`{c}_{f}=\mathrm{1,0}·{10}^{3}m/s`


Boundary conditions and loading
------------------------------------


.. code-block:: text

    * Movement only along the :math:`x` axis.


    * Embedding the pipe at the :math:`A` end.


    * Free tubing at the :math:`B` end.


    * For the fluid reservoir condition at the :math:`A` end.