28. Cable internal/structural damping

The identification tag for this tutorial is PDS-AAS. Pregenerated input files for this tutorial are found in the folder named PDS-AAS in the provided tutorial input files.

28.1. Tutorial overview

This tutorial covers:

  • Cable internal damping
  • Over-damping
  • Appropriate damping values
  • Automatic calculation of axial damping

28.2. Introduction to cable internal and structural damping

Note

  • Internal damping is a means of energy dissipation within a material, and can vary greatly depending on the material. Internal damping can be important to accurately replicate the dynamics of structures undergoing cyclic loading.
  • It is sometimes difficult to determine internal damping properties for materials, as they are usually not provided on material property sheets. The adaptive integrator used in ProteusDS is also very sensitive to internal cable damping, as it will adjust simulation time step to attempt to capture high frequency dynamics automatically.
  • Usually, these high frequencies do not affect system behavior in any important way, however they can result in slow simulation execution speed. In cases where cable damping does not affect the system behavior significantly, damping can be carefully chosen to optimize simulation speed.
  • Often, high frequency noise can be seen in cable tension history as the cable finite element lengths decrease. One way of mitigating the noise is to use internal structural damping. This mitigates high frequency noise, allowing larger time steps to be used and faster simulation execution speeds.
  • The properties $CID (axial coefficient of internal damping), $BCID (bending coefficient of internal damping), and $TCID (torsional coefficient of internal damping) can all be explicitly defined in the cable segment library feature to define internal cable damping.
  • Care must be taken in selecting the damping coefficients because values that are too high will over-damp the system, resulting again in a reduced time step and slow simulation execution.
  • Values must be selected that do not detrimentally affect the accuracy of the time domain response of the tensions at frequencies of interest.
  • Alternatively, the coefficient of axial internal damping $CID can be automatically determined by defining a reference axial damping ratio ($AxialReferenceDampingRatio).

28.3. Defining coefficients of internal damping

  • Open the Simulating a pendulum tutorial project file.
  • In the wire_rope_2in cable properties, set $AxialDampingMode 0 to allow for direct definition of the axial damping coefficient. Resolve follower properties. The $CID property will be added into the property list.
  • Set $CID 100. Leave $BCID and $TCID as 0.
  • The wire_rope_2in feature should appear as follows:
// Axial Rigidity
$AxialRigidityMode 0
$EA 2e8

// Fluid loading
$CDc 1.5
$CDt 0.01
$CAc 1

// Mechanical
$EI1 1e3
$EI2 1e3
$GJ 1e3
$Diameter 0.05
$Density 5000
$AxialDampingMode 1
$AxialReferenceDampingRatio 0.5
// $CID 100
$BCID 0
$TCID 0
$CE 1

// Strain Limit
$ElongationLimitMode 0

28.4. Running and visualizing a simulation with limited internal damping

  • Run the simulation for 30 seconds. Since the damping value is low, there may be high frequency noise seen in the cable tension. The adaptive numerical integrator will detect this and reduce the time step, thus resulting in a slow simulation speed.
  • Open PostPDS and plot the cable tension of element 1. The element tension history will show high spikes at the beginning of the simulation with continuing oscillations.

28.5. Consequences of over-damping

  • To eliminate the tension spikes and oscillations occurring in the cable, set $CID 1e7.
  • Rerun the simulation and notice that the simulation time step has decreased to such a small value that the simulation will take too long to complete.

28.6. Using appropriate damping values

  • Lower coefficient of internal damping with $CID 1e4.
  • Rerun the simulation and notice the speed in which the simulation is executing.
  • Visualize the results in PostPDS and plot the cable tension again.

Note

  • Notice that the tension spikes and oscillations have been mitigated.

28.7. Automatic calculation of axial damping

Note

  • As seen from the previous sections, simulation results and execution time is very sensitive to axial damping in cables.
  • Depending on the problem, it may be difficult or time consuming to determine the appropriate damping coefficients for all cables in a simulation.
  • Automatic calculation of axial damping can be specified by setting $AxialDampingMode to 1 and then supplying the damping ratio with $AxialReferenceDampingRatio.
  • The damping ratio (\(\zeta\)) is the ratio of the axial damping coefficient $CID to the critical axial damping coefficient. The critical damping factor is:
\(CID_{crit} = 2L\sqrt{Km}\)
  • \(K\) is the average stiffness of the cable elements acting on the nodes, \(m\) is the average cable node mass, and \(L\) is the average element length.
  • Corresponding damping coefficients are calculated on a cable segment basis, using average element stiffness, length, and cable node mass covered by said cable segment. Two different cables with the same specified DCableSegment feature may have different calculated damping coefficients depending on their respective average element lengths.
  • In the wire_rope_2in cable properties, set $AxialDampingMode 1 to allow for automatic calculation of axial damping. Resolve follower properties. The $AxialReferenceDampingRatio property will be added into the property list.
  • Set $AxialReferenceDampingRatio 0.5.
  • Rerun the simulation and view the results.