Introduction
============

The vibratory behavior of a structure is often modified if it is in the presence of a fluid: this is called vibro-acoustic coupling. Coupling cases are distinguished into two categories: either the fluid is infinite (this is the case of submerged structures), or the fluid is contained in a bounded medium (this is the case of reservoirs more or less filled with fluid).

The finite elements described here make it possible to solve coupling problems with a finite dimensional fluid.

**General notes:**


.. csv-table::

    ":math:`P`:", "instantaneous total pressure at a point in the fluid,"
    ":math:`{p}_{0}`:", "pressure at rest,"
    ":math:`p`:", "sound pressure,"
    ":math:`{\rho }_{t}`:", "instantaneous total density at a point in the fluid,"
    ":math:`{\rho }_{0}`:", "density of the fluid at rest,"
    ":math:`\rho`:", "acoustic density,"
    ":math:`{\rho }_{S}`:", "density of the structure,"
    ":math:`{\mathrm{u}}_{f}`:", "acoustic displacement,"
    ":math:`u`:", "moving the structure,"
    ":math:`\varphi`, :math:`\mathrm{\Phi }`:", "fluid displacement potential,"
    ":math:`\psi`, :math:`\mathrm{\Psi }`:", "fluid speed potential,"
    ":math:`\omega`, :math:`f`:", "pulsation, frequency,"
    ":math:`c`:", "speed of sound in the fluid,"
    ":math:`\lambda`, :math:`k`:", "wavelength, wave number,"
    ":math:`\sigma`:", "structure stress tensor,"
    ":math:`\varepsilon`:", "structural deformation tensor,"
    ":math:`C`:", "structural elasticity tensor,"
    ":math:`T`:", "fluid stress tensor."