Method Overview

The static shape of the structure needs to be found. The procedure will depend on the actual case and how it is modelled in RIFLEX, cf. the RIFLEX Theory and User Manuals. Once the static condition is found, the normal flow velocity \(\mathrm {U_N}\) along the structure is found from the current profile and shape of the structure.

The eigenfrequencies and mode shapes of the structure must be found. Added mass is initially applied as for a non-vibrating structure in still water according to standard RIFLEX input. The results will be given in terms of eigenvectors \(\mathrm {\phi _i}\) and associated eigenfrequencies \(\mathrm {\omega _i}\). A sufficient number of eigenvalues will be found so that all possibly active VIV frequencies can be found when considering the maximum vortex shedding frequency along the riser. The eigenvectors will be sorted into CF and IL groups, see Definition of IL and CF eigenvectors.

A subset of all calculated eigenfrequencies will define the complete set of possibly active eigenfrequencies. Added mass under VIV conditions will, however, become different from the still water values, and depend on the response frequency. Hence, iterations must be carried out for each eigenfrequency that is considered as a candidate for being excited by vortex shedding. This iteration is always needed for CF response, but also for pure IL. For IL in combination with CF, however, it is assumed that the IL frequency is two times the CF, which means that the iteration is not needed. The iteration has converged when there is consistence between the modified eigenfrequency and modified added mass distribution.

Each response frequency will be associated to an excitation zone where vortex shedding may excite the structure at the actual frequency. The zone is defined by an interval for the local non-dimensional frequency. Zones for the entire set of possible response frequencies may overlap. The definition of zones will therefore be different for a time sharing analysis and an analysis based on simultaneously active frequencies, see Multi Frequency Response. Pure IL response will have its zone defined in the same way as for CF, but IL in combination with CF will have the same excitation zone as for the associated CF response component.

Cases with sheared current will normally have more than one response frequency candidate.

This situation can have two different solutions:

The two options will lead to different definitions of the excitation zones:

Rules for the zone definition in such cases are defined in Multi Frequency Response.

The Frequency Response Method is used to calculate the dynamic response at the response frequencies found in Step 3 with excitation zoned defined in Step 4. The response analysis applies an iteration that converges when the response is in accordance with the non-linear models for excitation and damping forces. Both local response amplitude and phase between the local load and response are considered in this iteration.

The IL response is calculated in the same way as for CF, but all data for hydrodynamic coefficients are different. The complete solution for a general VIV case will hence consist of two complex response vectors, one at the double frequency of the other.

Fatigue damage is calculated on the basis of user defined SN curves and the calculated response. The Miner-Palmgren rule for damage accumulation is applied. Rainflow cycle counting is used if the ``simultaneously active frequencies'' option is assumed, while an analytical solution can be used for the time sharing case. For further details, see Fatigue Analysis.

Blevins’ and Vandiver’s equations for calculating drag magnification will be used for pure CF and combined IL/CF cases. Aronsen’s data from forced IL motion tests are used for pure IL response. For further details, see Drag Coefficient Modification.

Results are stored on VIVANA result files and files that can be presented by the VIVANA4WINDOWS user interface. In addition, VIVANA will produce files that can be used by RIFLEX STAMOD in an updated static analysis with amplified drag forces, or in a non-linear time domain analysis by RIFLEX DYNMOD. Use of these options is described in the RIFLEX User Manual.