| CU | Connector relative displacements/rotations. |
| CUE | Connector elastic displacements/rotations. |
| CEF | Connector elastic forces/moments. |
# Additional reference
• Genta, G., Dynamics of Rotating Systems, Springer, 2005.
# 31.2.3 CONNECTOR DAMPING BEHAVIOR
Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE
# References
• “Connectors: overview,” Section 31.1.1
• “Connector behavior,” Section 31.2.1
• \*CONNECTOR BEHAVIOR
• \*CONNECTOR DAMPING
• “Defining damping,” Section 15.17.2 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
# Overview
Connector damping behavior:
• can be of a dashpot-like viscous nature in transient or steady-state dynamic analyses;
• can be of a “structural” nature, related to complex stiffness, for steady-state dynamics procedures that support non-diagonal damping;
• can be defined in any connector with available components of relative motion;
• can be specified for each available component of relative motion independently, in which case the behavior can be linear or nonlinear for viscous nature damping;
• can be specified as dependent on relative positions or constitutive motions in several local directions for viscous nature damping; and
• can be specified for all available components of relative motion as coupled damping behavior.
The directions in which the forces and moments act and the relative velocities are measured are determined by the local directions as described in “Connection-type library,” Section 31.1.5, for each connection type. In dynamic analysis the relative velocities are obtained as part of the integration operator; in quasi-static analysis in Abaqus/Standard the relative velocities are obtained by dividing the relative displacement increments by the time increment.
# Defining linear uncoupled viscous damping behavior
In the simplest case of linear uncoupled damping you define the damping coefficients for the selected components $( \mathrm { i } . \mathrm { e } . , C _ { 1 1 }$ for component 1, $C _ { 2 2 }$ for component 2, etc.), which are used in the equation
$$
F _ {i} = C _ {i i} v _ {i} \quad (\text { no sum on } i),
$$
where $F _ { i }$ is the force or moment in the $i ^ { \mathrm { t h } }$ component of relative motion and $v _ { i }$ is the velocity or angular velocity in the $i ^ { \mathrm { t h } }$ direction. The damping coefficient can depend on frequency (in Abaqus/Standard),
temperature, and field variables. See “Input syntax rules,” Section 1.2.1, for further information about defining data as functions of frequency, temperature, and field variables.
If frequency-dependent damping behavior is specified in an Abaqus/Standard analysis procedure other than direct solution steady-state dynamics, the data for the lowest frequency given will be used.
Input File Usage: Use the following options to define linear uncoupled damping connector behavior:
\*CONNECTOR BEHAVIOR, NAME=name
\*CONNECTOR DAMPING, COMPONENT=component number,
DEPENDENCIES=n
Abaqus/CAE Usage: Interaction module: connector section editor: Add→Damping: Definition:
Linear, Force/Moment: component or components, Coupling: Uncoupled
# Defining linear coupled viscous damping behavior
In the linear coupled case you define the damping coefficient matrix components, $C _ { i j }$ , which are used in the equation
$$
F _ {i} = \sum_ {j} C _ {i j} v _ {j},
$$
where $F _ { i }$ is the force in the $i ^ { \mathrm { t h } }$ component of relative motion, $v _ { j }$ is the velocity in the $j ^ { \mathrm { t h } }$ component, and $C _ { i j }$ is the coupling between the $i ^ { \mathrm { t h } }$ and $j ^ { \mathrm { t h } }$ components. The $c$ matrix is assumed to be symmetric, so only the upper triangle of the matrix is specified. In connectors with kinematic constraints the entries that correspond to the constrained components of relative motion will be ignored. The damping coefficient can depend on temperature and field variables. See “Input syntax rules,” Section 1.2.1, for further information about defining data as functions of temperature and field variables.
Input File Usage: Use the following options to define linear coupled damping connector behavior:
\*CONNECTOR BEHAVIOR, NAME=name
$* { \mathrm { C O N N E C T O R ~ D A M P I N G } } , { \mathrm { D E P E N D E N C I E S } } = n$
Abaqus/CAE Usage: Interaction module: connector section editor: Add→Damping: Definition:
Linear, Force/Moment: component or components, Coupling: Coupled
# Defining unsymmetric linear coupled viscous damping behavior
As with linear coupled elastic behavior (“Connector elastic behavior,” Section 31.2.2), Abaqus/Standard allows you to define an unsymmetric coupled viscous damping matrix. In the linear coupled case you define the damping coefficient matrix components, $C _ { i j }$ , which are used in the equation
$$
F _ {i} = \sum_ {j} C _ {i j} v _ {j},
$$
where $F _ { i }$ is the force in the $i ^ { \mathrm { t h } }$ component of relative motion, $v _ { j }$ is the velocity in the $j ^ { \mathrm { t h } }$ component, and $C _ { i j }$ is the coupling between the $i ^ { \mathrm { t h } }$ and $j ^ { \mathrm { t h } }$ components. The C matrix is assumed to be unsymmetric, so the entire matrix is specified. The entries that correspond to the constrained components of relative
motion are ignored. When the unsymmetric matrix storage and solution scheme are used, the damping coefficients can depend on frequency, temperature, and field variables. See “Input syntax rules,” Section 1.2.1, for further information about defining data as functions of frequency, temperature and field variables.
Input File Usage: Use the following options to define unsymmetric linear coupled viscous damping connector behavior:
```txt
*CONNECTOR BEHAVIOR, NAME=name
*CONNECTOR DAMPING, UNSYMM,
FREQUENCY DEPENDENCE=ON
```
Abaqus/CAE Usage: Unsymmetric linear coupled viscous damping behavior is not supported in Abaqus/CAE.
# Defining nonlinear viscous damping behavior
For nonlinear damping you specify forces or moments as nonlinear functions of the velocity in the available components of relative motion directions, $F _ { i } ( v _ { 1 } , v _ { 2 } , \dots )$ . These functions can also depend on temperature and field variables. See “Input syntax rules,” Section 1.2.1, for further information about defining data as functions of temperature and field variables.
# Defining nonlinear viscous damping behavior that depends on one component direction
By default, each nonlinear force or moment function is dependent only on the velocity in the direction of the specified component of relative motion.
Input File Usage: Use the following options:
```txt
*CONNECTOR BEHAVIOR, NAME=name
*CONNECTOR DAMPING, COMPONENT=component number,
NONLINEAR, DEPENDENCIES=n
```
Abaqus/CAE Usage: Interaction module: connector section editor: Add→Damping:
```txt
Definition: Nonlinear, Force/Moment: component or components, Coupling: Uncoupled
```
# Defining nonlinear viscous damping behavior that depends on several component directions
Alternatively, the functions can depend on the relative positions or constitutive displacements/rotations in several component directions, as described in “Defining nonlinear connector behavior properties to depend on relative positions or constitutive displacements/rotations” in “Connector behavior,” Section 31.2.1.
Input File Usage: Use the following options to define nonlinear damping connector behavior that depends on components of relative position:
```txt
*CONNECTOR BEHAVIOR, NAME=name
*CONNECTOR DAMPING, COMPONENT=component number, NONLINEAR, INDEPENDENT COMPONENTS=POSITION, DEPENDENCIES=n
```
Use the following options to define nonlinear damping connector behavior that depends on components of constitutive displacements or rotations:
\*CONNECTOR BEHAVIOR, NAME=name
\*CONNECTOR DAMPING, COMPONENT=component number,
NONLINEAR, INDEPENDENT COMPONENTS=CONSTITUTIVE
MOTION, DEPENDENCIES=n
Abaqus/CAE Usage: Interaction module: connector section editor: Add→Damping: Definition:
Nonlinear, Force/Moment: component or components, Coupling:
Coupled on position or Coupled on motion
# Example
Refer to the example in Figure 31.2.3–1.
