Body

A Body is the basic component used to model ships, semisubmersibles, spar buoys or other floating structures.
Hydrodynamic properties, forces, couplings etc. are attached to SIMO Bodies.

1. Initial Position

The initial body position is the position of the body when the static simulation starts. If equilibrium is calculated the body might move which means that the position might be different when the dynamic simulation starts.

2. Body Type

The body type determines basic assumptions about the behaviour of the body and which force models are available for the body. Four options are available:

  • Prescribed: The body has a fixed or prescribed position.

  • 6 DOF - time domain: Total motion in six degrees of freedom is simulated in time domain.

  • 6 DOF - separated analysis: Wave frequency motions are simulated in frequency domain while other forces are simulated in time domain.

  • 3 DOF - time domain: Total motion in three degrees of freedom (translations) is simulated in time domain.

A description of each option is given below.

2.1. 6 DOF Time Domain Bodies

For bodies with type 6 DOF - time domain the total motion in six degrees of freedom is simulated in time domain. Any First Order Wave Force Transfer Function and Retardation Function is used during the simulation while any First Order Motion Transfer Function is ignored.

2.1.1. Estimation of Low Frequency Motion

Floating vessels can be modelled in two basic ways in SIMO:

  • Separated analysis, which works based on separation of wave frequency (WF) and low frequency (LF) motions. In this case the low frequency motion is directly available in the analysis.

  • Simulation of total motion, which solves the combined wave and low frequency motion in time without separation.

In some situations during the time domain simulation the low frequency motion of a body is needed. This is not directly available when simulating total motion in time domain so the low frequency motion has to be estimated based on the time series of total motion.

Estimation of low frequency motion is intended to be used for floating vessels with 1st and 2nd order hydrodynamic forces included, i.e. bodies that have wave force transfer functions and retardation functions.
For other bodies, for example spool pieces, templates etc. in a lifting operation, the estimation method should be set to No estimation or body type 2 may be used.

The low-frequency body position and velocity is used for several purposes, most notably:

  • Heading correction: When interpolating between force time series for different headings during simulation (heading correction), the low frequency yaw motion is used to obtain the relative wave heading and thereby the correct time varying force transfer function. If the total yaw motion is used, wave frequency temporal changes in the transfer function will interact with the wave and create fictitios difference-frequency forces. This may lead to, for example, wrong mean heading of a weather vaning vessel.

  • Cosine series waves: When calculating wave excitation forces together with the Cosine wave generation method, the phase of the wave force will be based on the low-frequency instantaneous position of the body.

  • Low-frequency damping: When defining linear and quadratic damping matrices, the user can choose between multiplying the matrix with low-frequency, wave-frequency or the total velocity.

  • Current force: Low-frequency velocity is used in calculation of relative current velocity

  • Wind force: Low-frequency velocity is used in calculation of relative current velocity

There are currently two alternative methods for estimating low-frequency motions:

  • 2nd order low-pass (LP) Butterworth filter

  • Non-linearity-pass (NLP) filter based on 1st order motion transfer functions

Estimation of low frequency motion is intended to be used for floating vessels, i.e. bodies that have a wave force transfer function. For bodies that do not have wave a wave force transfer function - for example spool pieces, templates etc. in a lifting operation - no estimation will be used.

The primary disadvantage of using the Butterworth filter is that a significant delay will be introduced in the LP filtered signals. Moreover, the filter have a mild roll-off, meaning that it will not be able to remove all the energy above the cut-off frequency. The delay can lead to undesired and unphysical effects. One effect is that a low-frequency damping force will have a component in phase with displacement, thereby acting as an apparent stiffness and modifying the natural period of the system. It has also been observed that the heading stability of turret moored vessels can be adversely affected by the delay. An increase in cut-off period will increase the delay, and this has shown to increase the magnitude of unstable yaw motion. To limit the delay, it is therefore advised to use a cut-off period close to the wave frequency range. A reasonable starting point can be,

\[T_c = 2.5 \cdot T_P\]

where \(T_c\) is the cut off period and \(T_P\) is the peak period of the irregular wave spectrum

The non-linearity-pass (NLP) filter estimates the LF motion by subtracting the linear wave induced motions from the total
motion. The linear motion is obtained from first order motion transfer functions (RAO’s). As such, it has much in common
with the separated analysis option (body type 2). The main
advantage of simulating the total motion (body type 1) in combination with an NLP filter as compared to body type 2, is that
body type 1 will capture interactions between the wave frequency responses and the low frequency responses. Such
interactions will in principle exist in all nonlinear systems.

The NLP filter will work well (as a low-pass filter) when the following conditions are met:

  • The wave frequency range of the simulated response is dominated by linear wave induced response.

  • The provided 1st order motion transfer functions (RAO’s) are accurate and represents a linearization of the SIMO simulation model

  • The effect of LF response on the WF response is small.

  • Low frequency (difference-frequency) non-linear responses is much larger than high frequency (sum-frequency) responses.

These conditions are most often satisfied for a large volume floating structure subjected to waves and the NLP filter is then the recommended filtering method. The best way to determine the applicability is by comparing time series and power spectra of total and LF motions estimated by SIMO. It should be noted that in many cases there will be a significant effect of the WF responses on the LF responses - an effect not captured by a separated analysis (body type 2). The presence of such effects does not make the filter less efficient. An opposite effect (LF effect on WF responses) will however violate the conditions listed above and make the filter less efficient. Still, even in cases where the conditions are only approximately satisfied the filter may remove most of the wave frequency responses and perform satisfactorily. Indeed it is likely to remove a larger portion of the WF responses as compared to the Butterworth filter due to the mild roll-off the Butterworth filter.

It should be noted that the wave frequency response subtracted from the total response is itself dependent on the low-frequency yaw motion. Thus, the LF yaw angle,

\[\psi_{LF}\]

, is calculated by solving the following non-linear equation for

\[\psi_{LF}\]

:

\[\psi_{LF} = \psi - \psi_{WF}(\psi_{LF})\]

This equation will have a unique solution when

\[\frac{d\psi_{WF}(\psi_{LF})}{\psi_{LF}} < 1\] 
for all
\[\psi_{LF}\]

.

2.2. 6 DOF Separated Analysis Bodies

When using separated analysis the wave frequency motions are solved separated from other force models. It may be used when the wave frequency motions are not affected by other external or internal forces like mooring line forces. In this case the First Order Motion Transfer Function is used to calculate wave frequency motion. If the body also has a Wave Force Transfer Function and a Retardation Function these will not be used during the simulation.

Separated analysis is most commonly used in the following cases:

  • When simulating a vessel in situations where low frequency motions can be neglected

  • As an alternative to total time domain simulation for station keeping analyses of vessels moored with a slack catenary system

2.3. 3 DOF Time Domain Bodies

Bodies of this type has three translational degrees of freedom. Bodies of this type may use the Small Body Hydrodynamics force model.

2.4. Prescribed Bodies

Three options are available for prescribed bodies:

  • Fixed position: The body is fixed at its initial position during the whole simulation.

  • Read from file: The body follows the position time series in the specified file.

  • Articulated structure: The body is fixed to a master body. Additionally, a predefined motion may be specified for one degree of freedom. This can for example be used to model a moving crane.

2.4.1. Positions Read from File

Time series of the body position can be read from a text file with the following format:

6
NSAMPLES
DT
XG1  YG1  ZG1  PHI1  THETA1  PSI1
XG2  YG2  ZG2  PHI2  THETA2  PSI2

Here

  • NSAMPLES: The number of samples in the time series

  • DT: The time step between each sample

  • XGi: real: Global X-coordinate of body \(\mathrm{[m\)}]

  • YGi: real: Global Y-coordinate of body \(\mathrm{[m\)}]

  • ZGi: real: Global Z-coordinate of body \(\mathrm{[m\)}]

  • PHIi: real: Euler angle, rotation about x-axis \(\mathrm{[deg\)}]

  • THETAi: real: Euler angle, rotation about y-axis \(\mathrm{[deg\)}]

  • PSIi: real: Euler angle, rotation about z-axis \(\mathrm{[deg\)}]

A complete example of a file with three samples with a time step of 1.0 seconds is given below:

6
3
1.0
0.0 0.0 0.0 0.0 0.0 0.0
1.0 2.0 3.0 4.0 5.0 6.0
1.0 2.0 3.0 4.0 5.0 6.0

2.4.2. Articulated Structure

An articulated structure is a body that is fixed to another body (master body) and will follow the master body during the simulation. Series of articulated structures can be specified to model movable mechanisms such as A-frames, cranes and gangways. Prescribed motion can be specified for each member of such a mechanism. The figure below shows an example of how a crane may be modelled as an articulated structure.

image

When using articulated structures it is important to consider the following limitations of the model:

  • The mechanism is a series of linked master / slave members

  • The main master (support body) of the articulated structure cannot itself be specified as an articulated structural member

  • Each of the members has its own body-fixed coordinate system

  • The link between a master and a slave member cannot be disconnected

  • The relative motion (translation or rotation) between the slave and the master can only take place along or around one of the principle axis of master’s coordinate system

  • The series of bodies should not be arranged in loops