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General viscous damping
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The general viscous damping property implements a viscous damping between the source and target interface.

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Definition
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Source and target interfaces can be chosen arbitrarily.

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Parameters
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General link couplings can be parametrised in two modes: `simple` and `advanced`, which are described in the following.

^^^^^^^^^^^^^
Advanced mode
^^^^^^^^^^^^^

In the advanced mode, the user is prompted to supply four damping matrices, :math:`\mathbf{D_{SS}}`, :math:`\mathbf{D_{ST}}`, :math:`\mathbf{D_{TS}}`, and :math:`\mathbf{D_{TT}}`. Following equation describes how the stiffness matrices define a coupling between the target and source interface, denoted by subscript :math:`{T}` and :math:`{S}`, respectively.

.. math::

   \begin{bmatrix}\mathbf{F_T} \\ \mathbf{F_S} \end{bmatrix} = \begin{bmatrix}\mathbf{D_{TT}} & \mathbf{D_{TS}} \\ \mathbf{D_{ST}} & \mathbf{D_{SS}}\end{bmatrix} \, \begin{bmatrix} \dot{\mathbf{y}}_\mathbf{T} \\ \dot{\mathbf{y}}_\mathbf{S} \end{bmatrix}

A list of symbols is shown in following table.

===================================  =================================  ===========================================================
Symbol                               Dimension                          Meaning                                                    
===================================  =================================  ===========================================================
:math:`\mathbf{F_T}`                 :math:`\in\mathbb{R}^{6\times 1}`  Load vector to target interface                                              
:math:`\mathbf{F_S}`                 :math:`\in\mathbb{R}^{6\times 1}`  Load vector to target interface                                              
:math:`\dot{\mathbf{y}}_\mathbf{T}`  :math:`\in\mathbb{R}^{6\times 1}`  Displacement vector of target interface                                      
:math:`\dot{\mathbf{y}}_\mathbf{S}`  :math:`\in\mathbb{R}^{6\times 1}`  Displacement vector of source interface                                      
:math:`\mathbf{D_{TT}}`              :math:`\in\mathbb{R}^{6\times 6}`  Damping matrix coupling target displacement and target load                
:math:`\mathbf{D_{ST}}`              :math:`\in\mathbb{R}^{6\times 6}`  Damping matrix coupling target displacement and source load                
:math:`\mathbf{D_{TS}}`              :math:`\in\mathbb{R}^{6\times 6}`  Damping matrix coupling source displacement and target load                
:math:`\mathbf{D_{SS}}`              :math:`\in\mathbb{R}^{6\times 6}`  Damping matrix coupling source displacement and source load                
===================================  =================================  ===========================================================

^^^^^^^^^^^
Simple mode
^^^^^^^^^^^

In the simple mode, a symmetric behaviour between target and source interface is implied. The four damping matrices are replaced by a single damping matrix :math:`\mathbf{D}` and applied to the coupling equation as follows:
   
.. math::

   \begin{bmatrix}\mathbf{F_T} \\ \mathbf{F_S} \end{bmatrix} = \begin{bmatrix}\mathbf{D} & -\mathbf{D} \\ -\mathbf{D} & \mathbf{D}\end{bmatrix} \, \begin{bmatrix} \dot{\mathbf{y}}_\mathbf{T} \\ \dot{\mathbf{y}}_\mathbf{S} \end{bmatrix}