Riser VIV Axial Fatigue Analysis and Mathieu instability Mitigation
Authors: Zhang Libang , Eltaher Ayman , Jukes Paul 
Published: April 2012

Abstract
Currently, the so-called state-of-practice approaches are commonly used inriser VIV analysis. DNV RP F204 has indicated that riser axial stress fatiguedue to VIV is not considered due to the limitation of the state-of-practiceapproach. This paper gives a methodology for considering the top tensionedriser (TTR) axial stress fatigue due to VIV, using nonlinear coupledbeam-column modeling, and proposes a procedure, using Flexcom and Shear7, toconduct TTR axial stress fatigue damage analysis. Case studies are discussed, including TTR VIV in the Gulf of Mexico (GoM) and West of Africa (WoA).
On the other hand, API RP 2RD suggests that TTR with relatively stifftensioning systems may experience tension fluctuations that are significantrelative to the mean tension, leading to significant changes in the lateralstiffness. Further, it was found in field tests in Norway that if VIV frequencycoincides with half the TTR axial mode frequency, extreme axial stressesresult. This paper demonstrates that the phenomenon observed in the field testis due to the Mathieu effects. Using Mathieu theory on TTR axial stressresonance due to VIV is a novel idea and this paper provides a novelmethodology to assess Mathieu Instability (MI), specifically, stabilitydiagrams with damping effects in parameter plans are generated. These diagramsare intended to cover possible combinations of TTR properties, such aspre-tension, mass, damping, axial and bending stiffness etc. Finally, thispaper illustrates applications of new method in total VIV fatigue analysis, including axial fatigue, and MI engineering assessment.

Introduction
In offshore oil exploration and development, fatigue damage associated with VIVposes significant challenges in the TTR design. MARINTEK has carried out largescale riser model testing (Huse, et al., 1998) and research on VIV inducedriser axial vibrations (Huse et al. 1999). During their model testing in Fjordsin Norway, unexpected considerable riser tension fluctuations due to VIV werefound. Based on their investigations, it was found that if VIV frequencycoincides with half the frequency of the first axial vibratory mode of theriser, extreme stresses occur. This paper presents a theory that explains theTTR axial fatigue based on the physical mechanism of MI.
At present, the state-of-practice in riser VIV fatigue analysis is the Shear7software. DNV-RP-F204 (DNV, 2010) indicates that the limitation ofstate-of-practice approach is that axial stress damage due to VIV is notincluded due to the complexity of its nonlinear nature. Also it indicates thatTTR axial stress due to cross-flow VIV analysis would require a nonlinear timedomain analysis. This paper proposes a methodthat combines a dynamic finiteelement software (such as Flexcom) with Shear7, for the calculation of TTRaxial stress fatigue due to VIV. In this paper the proposed theory is appliedto a TTR to predict both axial and bending fatigue life. First, cross-flow VIVresponse is predicted using Flexcom and Shear7, then forced axial vibrationsolutions are derived and solved using simple (e.g., MATLAB) programming.