# Analysis Procedure

This chapter gives a short overview of the tasks `VIVANA`

carries out in
an analysis of VIV response. For further details on the specific task the
VIVANA Theory Description should be consulted.

The analysis method is based on a three dimensional (3D) finite element formulation that in principle may take any 3D effects into account. The element theory is described in the RIFLEX Theory Description. A brief outline of the analysis procedure is given in the following.

## 1. Step 1. Static analysis

The static shape of the structure needs to be found. The procedure will
depend on the actual system and how it is modelled in `RIFLEX`

.

## 2. Step 2. Eigenvalue analysis

The eigenfrequencies and mode shapes of the structure are found. Added mass is initially applied as for a non-responding riser in still water according to data given by the user. The results will be given in terms of discrete eigenvectors \(\mathrm {\phi _i}\) and associated eigenfrequencies \(\mathrm {\omega _i}\) \(\mathrm {[rad/s]}\) or \(\mathrm {f_i}\) \(\mathrm {[Hz]}\). A sufficient number of eigenvalues will be found so that all possibly active frequencies can be found when considering the maximum vortex shedding frequency along the structure.

## 3. Step 3. Identification of possible and dominating excitation frequencies

A subset of all calculated eigenfrequencies will define the complete set of possibly active eigen-frequencies. Added mass under VIV conditions will, however, become different from the still water case as applied for the initial eigenvalue analysis. Hence, iterations must be performed for each frequency candidate in order to find a set of possible response frequencies. The iteration has converged when there is consistency between the modified eigenfrequency and modified added mass distribution. Each response frequency candidate will be associated with an excitation zone, and the dominating response frequency will be identified among the candidates according to the theory described herein.

## 4. Step 4. Analysis of the response at the dominating frequency

The frequency response method is used to calculate the dynamic response at the dominating frequency identified in step 3. The user may also specify which frequency that should be selected as the dominating response frequency. The analysis applies an iteration that converges when the response is in accordance with the nonlinear models for excitation and damping. Both local response amplitude and phase are considered in this iteration.

## 5. Step 5a. Response analysis for other frequencies than the dominating frequency - concurrent response frequencies

In case of a strongly sheared profile the result from Step 4 may show an excitation zone for the dominating frequency that does not cover the total length of the structure. Consequently excitation may take place at other frequencies in zones outside the identified zone. A similar analysis as for Step 4 must now be carried out for each frequency, but the excitation zone will now become the original zone for the new frequency with a reduction according to the zone taken by the more dominating frequencies. Note that if the user decides to apply another frequency than the program as the dominating response frequency, the resulting response will be influenced since another frequency will be given the privilege of occupying its total potential excitation zone.

## 6. Step 5b. Response analysis for other frequencies than the dominating frequency - consecutive response frequencies

The procedure described in Step 4 will be repeated for the other response frequencies that may be excited. Each response frequency will have its complete excitation zone, but will only be active part of the time.

## 7. Step 6. Post-processing of results

Post-processing includes fatigue analysis and calculation of amplified drag coefficients.

In addition to the analysis procedure outlined above, the program will present results from an evaluation of the actual riserâ€™s performance regarding VIV, see the section Input to VIVANA.

As mentioned before it is possible to proceed to a Step 7 that will
carry out an updated static analysis with amplified drag forces
according to the results from `VIVANA`

. It is also possible to use the
`RIFLEX`

`DYNMOD`

module to carry out an improved dynamic analysis by
using intermediate results from `VIVANA`

in a nonlinear time domain
model. This option is not available in the standard `VIVANA`

program.
For further details, see Larsen et.al. (2004).