Hydrodynamic cable

A cable object with dynamic stiffness and hydrodynamic loading.

Collaboration diagram for Hydrodynamic cable:

Author

Karl-Johan Reite

This class simulates a cable object consisting of one or more elements. Each element is of type CableElDynStiff. Each element has methods to make it possible to use larger time steps in the integration. This is done by decreasing the stiffness of the element until the eigenfrequency of the element is low enough for the integration to be performed with the defined maximum step size.

Each element is regarded as a straight segment, responsible for calculating the forces acting on each of its ends, as well as the mass associated with each end node. The forces and mass from each element is added to the corresponding nodes of the cable, and the acceleration of each node is calculated in the OdeFcn.

The cable is influenced by:

• Internal stiffness
• Internal damping
• Hydrodynamic normal and tangential forces
• Buoyancy and gravity
• Added mass

The calculation of these forces are more thoroughly explained in CableElDynStiff.

Example configuration excerpt

<Lib
   LibName          = "marine_elements"
   SimObject        = "Cable/LumpedMass"
   Name             = "C"
   NumElements      = "7"
   Density          = "3000"
   NumericalDamping = "0"
   Diameter         = "0.1"
   E                = "117"
   DampingRatio     = "1"
   FluidRho         = "1025"
   MaxStepLength    = "0.01"
   MaxTension       = "1000"
   MaxAcceleration  = "1005"
   StepSafetyFactor = "50"
   MeanTension      = "0"
   AdaptationPeriod = "0"
   MaterialName     = "Trawl/Wire2"
   NumFaces         = "5"
   DrawScale        = "2"
/>

Input Ports

Name	Width	Description
Length	1	The length of the cable.
PosA	3	The position of end A.
PosB	3	The position of end B.
VelA	3	The velocity of end A.
VelB	3	The velocity of end B.

There is no water-velocity input port. The ambient current is taken from the Environment shared resource, which the cable queries at the mid-point of each element.

Output Ports

Name	Width	Description
ForceA	3	The force from end A of the cable.
ForceB	3	The force from end B of the cable.
PosA	3	The position of end A.
PosB	3	The position of end B.

Configuration parameters

Name	Width	Description
NumElements	1	Number of internal mass elements (Default: 2).
Density	1	The density of the cable [kg/m³].
NumericalDamping	1	Added numerical damping on each node. The damping force is calculated as \(\vec F_i = -k m_i \vec v_i\), where \(\vec F_i\) is the added damping force, \(k\) is the numerical damping factor, \(m_i\) is the node inertia and \(\vec v_i\) is the velocity of the node (Default: 0).
Diameter	1	Diameter of the cable.
E	1	The Young's modulus (elasticity) of the cable.
DampingRatio	1	The relative axial damping of the cable. 0 is no damping, 1 is critical damping (Default: 1).
FluidRho	1	The density of the ambient fluid (Default: 1025).
MaxStepLength	1	Controls the stiffness of the cable to allow integration with step lengths up to this value (Default: 0.01).
MaxTension	1	The maximum tension. If above this value, the tension is set to this this value.
MaxAcceleration	1	The maximum acceleration. If above this value, the acceleration is set to this value (Default: 1000).
StepSafetyFactor	1	A safety factor between the MaxStepLength and the one used for calculating the stiffness of the cable (Default: 50).
MeanTension	1	Possibility to add a mean tension to correct for decreased stiffness of the cable (Default: 0).
AdaptationPeriod	1	If above zero, this tells the cable to correct its initial length to avoid length errors because of decreased stiffness (Default: 0).
MaterialName	1	The material to use for visualizing the cable (Default: Trawl/Wire2).
NumFaces	1	The number of planes to visualize the cable surface (Default: 5).
DrawScale	1	The scale of the visual appearance of the cable. This is used to make it more visible (Default: 2).

Initial conditions

This simObject does not have any initial conditions.

Full example file

<Contents>
   <OBJECTS>
      <Lib
         LibName          = "marine_elements"
         SimObject        = "Cable/LumpedMass"
         Name             = "C"
         NumElements      = "7"
         Density          = "3000"
         Diameter         = "0.1"
         E                = "117"
         MaxTension       = "1000"
      />
 
      <Lib
        LibName="environment"
        SimObject="Environment"
        Name="Env"
        Waves.Model="Component"
        Waves.NumWaves="0"
        Bathymetry.Depth="190"
        Current.Model = "Constant"
        Current.Vector = "2.5,0,0"
        />
   </OBJECTS>
 
   <INTERCONNECTIONS>
      <Connection
         C.PosA         = "0,0,0"
         C.VelA         = "0,0,0"
         C.PosB         = "0,0,18"
         C.VelB         = "0,0,0"
         C.Length       = "20"
      />
   </INTERCONNECTIONS>
 
   <INITIALIZATION>
      <InitialCondition
      />
   </INITIALIZATION>
 
   <SIMULATION>
      <Timing TStart="0" TEnd="30"/>
      <Integrator Method="RK45_i" LogStates="0" UseRSSNorm="0">
        <StepControl StepMax="0.1" StepMin="1E-060" AbsTol="0.001" RelTol="0.001"/>
      </Integrator>
   </SIMULATION>
</Contents>

This SimObject is referred to as Cable/LumpedMass