Connector Damping Behavior

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 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.

This page discusses:

Defining Linear Uncoupled Viscous Damping Behavior
Defining Linear Coupled Viscous Damping Behavior
Defining Unsymmetric Linear Coupled Viscous Damping Behavior
Defining Nonlinear Viscous Damping Behavior
Example
Defining Linear Structural Damping Behavior
Defining Connector Damping Behavior in Linear Perturbation Procedures
Output

Defining Linear Uncoupled Viscous Damping Behavior

In the simplest case of linear uncoupled damping you define the damping coefficients for the selected components (i.e., $C_{11}$ for component 1, $C_{22}$ for component 2, etc.), which are used in the equation

F_{i} = C_{i i} v_{i} (no
  sum
  on i),

where $F_{i}$ is the force or moment in the $i^{th}$ component of relative motion and $v_{i}$ is the velocity or angular velocity in the $i^{th}$ direction. The damping coefficient can depend on frequency (in Abaqus/Standard), temperature, and field variables. See Input Syntax Rules for further information about defining data as functions of frequency, temperature, and field variables.

In most cases if frequency-dependent damping behavior is specified in an Abaqus/Standard analysis procedure, the data at zero frequency is used. The exceptions are direct-solution steady-state dynamics, subspace-based steady-state dynamics, and natural or complex eigenvalue extraction.

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 $i^{th}$ component of relative motion, $v_{j}$ is the velocity in the $j^{th}$ component, and $C_{i j}$ is the coupling between the $i^{th}$ and $j^{th}$ 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 for further information about defining data as functions of temperature and field variables.

Defining Unsymmetric Linear Coupled Viscous Damping Behavior

As with linear coupled elastic behavior (Connector Elastic Behavior), 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 $i^{th}$ component of relative motion, $v_{j}$ is the velocity in the $j^{th}$ component, and $C_{i j}$ is the coupling between the $i^{th}$ and $j^{th}$ 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 for further information about defining data as functions of frequency, temperature and field variables.

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 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.

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.

Example

Refer to the example in Figure 1.

In addition to the torsional spring resisting relative rotations, the shock absorber damps translational motion along the line of the shock with a dashpot. To include a nonlinear dashpot behavior that is dependent on the relative position between the attachment points, use the following input:

CONNECTOR BEHAVIOR, NAME=sbehavior
...
CONNECTOR DAMPING, COMPONENT=1,
 INDEPENDENT COMPONENTS=POSITION, NONLINEAR
1
1500.0, 0.1, 0.0
1625.0, 0.2, 0.0
1750.0, 0.1, 10.0
1925.0, 0.2, 10.0

Defining Linear Structural Damping Behavior

Structural connector damping is supported in steady-state dynamics and modal transient procedures that support non-diagonal damping (for example, direct solution steady-state dynamics).

Defining Linear Uncoupled Structural Damping Behavior

You define the damping coefficients, $s_{j j}$ , for the selected components (i.e., $s_{11}$ for component 1, $s_{22}$ for component 2, etc.), which are used in the equation

F_{j} = i D_{j j} u_{j},

where

D_{j j} = s_{j j} K_{j j} (no
  sum
  on j)

is the structural damping matrix, $F_{j}$ is the imaginary part of the force or moment in the $j^{th}$ direction of relative motion, $u_{j}$ is the displacement in the $j^{th}$ direction, and $K_{j j}$ is the stiffness matrix. The damping coefficient can depend on frequency.

Defining Linear Coupled Structural Damping Behavior

You define 21 $s_{l j}$ damping coefficients (the symmetric half of the 6 × 6 damping coefficient matrix), which are used in the equation

F_{l} = i D_{l j} u_{j},

where

D_{l j} = i s_{l j} K_{l j} (no
  sum
  on l, j)

is the structural damping matrix, $F_{l}$ is the imaginary part of the force in the $l^{th}$ direction of relative motion, $u_{j}$ is the displacement in the $j^{th}$ direction, and $K_{l j}$ is the stiffness matrix. The damping coefficient matrix cannot depend on frequency.

Defining Connector Damping Behavior in Linear Perturbation Procedures

In both the direct-solution and subspace-based steady-state dynamic procedures, the viscous or structural damping defined using an uncoupled connector damping behavior may be frequency dependent. In other linear perturbation procedures connector damping behavior is ignored.

Output

The Abaqus output variables available for connectors are listed in Abaqus/Standard Output Variable Identifiers and Abaqus/Explicit Output Variable Identifiers. The following output variables are of particular interest when defining damping in connectors:

CV: Connector relative velocities/angular velocities.
CVF: Connector viscous forces/moments.