Spectral Formulations for Vortex Induced Vibration Modal Decomposition and Reconstruction

Abstract

Modal decomposition and reconstruction (MDR) of marine riser vortex induced vibration (VIV) is a technique where vibration is measured using accelerometers and/or angular rate sensors, the modal displacements are solved for and the stress and fatigue damage is reconstructed along the riser. Recent developments have greatly increased the accuracy and reliability of the method. However the computational burden is onerous due to stress time history reconstruction and rainflow cycle counting at every desired location along the riser. In addition, fully synchronous data are required to reconstruct the stress histories. Dirlik’s method for obtaining rainflow damage for Gaussian random stress using only spectral information (four spectral automoments) has proven to be quite accurate with a significant reduction in computational effort. In this paper two spectral formulations of MDR are introduced. The first method is applicable when all the measured data are synchronous. In this method, spectral cross moments of the modal displacements are solved from the spectral cross moments of the measured data using basis vectors consisting of normal mode shapes. The spectral automoments of stress are obtained from the modal displacement cross moments and analytical stress mode shapes. Dirlik’s method is then applied to obtain rainflow damage. The second method is a generalization of the first, where the measured data cross moments are only partially known. This method is applicable when measured data are partially synchronous or asynchronous. A numerical root-finding technique is employed to solve for the modal response cross moments. The method then proceeds in the same manner as the first. The spectral methods are applied to simulated VIV data of a full-scale deepwater riser and to Norwegian Deepwater Program (NDP) scale-model test data on a 38 m long slender riser. Comparisons of reconstructed fatigue damage versus simulated or measured damage indicate that the method is capable of estimating fatigue damage accurately for Gaussian VIV even when data are not fully synchronous. It is also shown that computational cost is greatly reduced.