# Dynamic analysis

OrcaFlex offers two approaches to dynamic analysis: frequency domain and time domain.

## Frequency domain dynamic analysis

Frequency domain analysis is linear. Any nonlinearites present are approximated to be linear by the frequency domain solver in a process known as linearisation.

The frequency domain solver uses the result of the static analysis as the system's configuration at which to generate linear transfer functions that map the underlying stochastic environmental (e.g. the wave elevation) or loading process to the system's response process. Because the system is defined by its static state, frequency domain analysis is not appropriate for analysing time-varying operations.

These linear transfer functions are used to calculate the system's response at each frequency of interest. The linearisation of the quadratic viscous drag load requires this process to be conducted iteratively until a converged solution is found.

The frequency domain solver can be used to solve at either wave frequency or low frequency solution frequencies.

Because of the stochastic nature of frequency domain analysis, the primary results output are statistics and spectral density. It is also possible to synthesise time histories from the frequency domain solution, although this is primarily intended for qualitative inspection of the result.

Frequency domain analysis can be considerably more efficient than time domain analysis. However, because of the constraints on the linearity and time-invariance of the system, frequency domain analysis is more limited in its applicability.

## Time domain dynamic analysis

Time domain analysis is fully nonlinear. Mass, damping, stiffness, loading etc. are evaluated at each time step, taking into account the instantaneous, time-varying geometry. Two time domain integration schemes are available: implicit and explicit.

Both integration schemes use numerical time-stepping algorithms to solve the equations of motion in the time domain. The dynamic simulation uses the static analysis as its initial configuration and time then evolves forward from there. For time domain analysis, the primary results output are time histories of response variables.

### Time and simulation stages

The period of simulation is defined as a number of consecutive stages, the durations of which are specified in the data. Various controlling aspects of the model can be set on a stage-by-stage basis, for example the way winches are controlled, the velocities and rates of turn of vessels and the releasing of lines, constraints, links and winches. This allows quite complex operational sequences to be modelled.

Before the main simulation stage(s) there is usually a build-up stage, during which wave and vessel motions are smoothly ramped up from zero to their full size. This gives a gentle start to the simulation and helps reduce the transients that are generated by the change from the static position to full dynamic motion. This build-up stage is usually numbered 0, and its length should normally be set to at least one wave. The ramping period can be controlled precisely by setting the ramp start time and ramp finish time on the general data form. The remaining stages, usually numbered 1, 2, 3, … are intended as the main stages of analysis.

Time is measured in OrcaFlex in seconds. To allow you to time-shift one aspect of the model relative to the others, different parts of the OrcaFlex model have their own user-specified time origins. See the diagram below.

For example, simulation time is measured relative to the simulation time origin, which is specified on the wave page on the environment data form. The simulation time origin, $t=0$, is usually at the end of the build-up stage, so negative simulation time is the build-up stage and the remaining stages are in positive simulation time. The figure below shows a simulation using a build-up of 10 seconds, followed by two stages of 15 seconds each.

Each wave train also has its own time origin, and similarly for time-varying and full field wind and any time history data that you use. All of these time origins are defined relative to the global time origin, so if necessary you can use the time origins to time-shift one aspect of the model relative to the others. The global time origin itself is not user-specified: since everything is relative to it, it is entirely arbitrary.

By default all of the time origins are zero, so all of the time frames coincide with global time. For most cases this simple situation is all you need, but you might, for example, want to arrange that a wave crest, or a particularly large wave in a random sea, arrives at your vessel at a particular point in the simulation. If you use the view profile facility and find that the wave arrives at the vessel at global time 2590s, then you can arrange that this occurs at simulation time 10s (i.e. 10 seconds into stage 1) by either

The former shifts the simulation forwards to when the wave occurs, whereas the latter shifts the wave back to the period the simulation covers.

 Figure: Time and simulation stages