General viscous damping¶
The general viscous damping property implements a viscous damping between the source and target interface.
Definition¶
Source and target interfaces can be chosen arbitrarily.
Parameters¶
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, \(\mathbf{D_{SS}}\), \(\mathbf{D_{ST}}\), \(\mathbf{D_{TS}}\), and \(\mathbf{D_{TT}}\). Following equation describes how the stiffness matrices define a coupling between the target and source interface, denoted by subscript \({T}\) and \({S}\), respectively.
A list of symbols is shown in following table.
Symbol |
Dimension |
Meaning |
|---|---|---|
\(\mathbf{F_T}\) |
\(\in\mathbb{R}^{6\times 1}\) |
Load vector to target interface |
\(\mathbf{F_S}\) |
\(\in\mathbb{R}^{6\times 1}\) |
Load vector to target interface |
\(\dot{\mathbf{y}}_\mathbf{T}\) |
\(\in\mathbb{R}^{6\times 1}\) |
Displacement vector of target interface |
\(\dot{\mathbf{y}}_\mathbf{S}\) |
\(\in\mathbb{R}^{6\times 1}\) |
Displacement vector of source interface |
\(\mathbf{D_{TT}}\) |
\(\in\mathbb{R}^{6\times 6}\) |
Damping matrix coupling target displacement and target load |
\(\mathbf{D_{ST}}\) |
\(\in\mathbb{R}^{6\times 6}\) |
Damping matrix coupling target displacement and source load |
\(\mathbf{D_{TS}}\) |
\(\in\mathbb{R}^{6\times 6}\) |
Damping matrix coupling source displacement and target load |
\(\mathbf{D_{SS}}\) |
\(\in\mathbb{R}^{6\times 6}\) |
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 \(\mathbf{D}\) and applied to the coupling equation as follows: