Evaluation of Axial and Lateral Modal Superposition for General 3D Drilling Riser Analysis
Authors: Burgdorf O. 
Published: October 2008

Abstract
A 3D partially non-linear transient filly-coupled riser analysis method is evaluated which uses modal superposition of independently extracted lateral and axial modes. Many lateral modes are combined with a lesser number axial modes to minimize adverse time step requirements typically induced by axial flexibility in direct time integration of beam-column elements. The reduced computer time option enables much faster parametric analysis of hang-off, as well as other connected drilling environments normally examined. Axial- Iateral coupling is explicitly enforced and, resonance fidelity is preserved when excitation is near or coincident with axial natural periods. Reasonable correlation is shown with envelopes of test case dynamic responses published by API. Applicability of the method is limited by linearity assumptions indigenous to modal representation of dynamic deflections relative to a mean deflected shape. Sensitivities of incipient buckling during hang-off to axial damping and stiffness aredescribed for an example 6000 ft. deep composite drilling riser system.

Introduction
Numerical simulation of advanced composite drilling riser structural response in deeper depth environments will potentiality require increasing inclusion of axial-lateral dynamic coupling to support development of design requirements. This coupling is most significant to simulation of hang-off environments. Advanced composite materials have attracted serious attention due to their favorable strength to weight ratios so important to deeper depth drilling riser systems.12 However, composite riser joints must be designed with sensitivity to axial dynamics that are potentially more adverse than predicted for steel joints. The substantial by lower axial stiffness of composite drilling riser joints causes these systems to have axial natural periods closer to wave excitation periods than corresponding steel systems. Fig, 1 describes natural lateral and axial periods for an example 6000 ft. deep composite drilling riser system which is rigidly (axially) connected to a drilling ship in a hang-off condition. Lateral (end-constrained) modes 6 through 19 exist within the dominant range of the wave spectrum. However, the fundamental (top-constrained) axial period is below the wave excitation range and minor axial excitation should be expected. Fig. 2. shows the effect of compliance added at the ship interface, causing the natural periods to increase into the wave excitation range. The same trend may be caused by a multitude of reasons including composite material or lay-up variations, emergency hang-off, heavier joints or increase in drilling depth. We are here concerned with making preliminary assessments of potentially adverse dynamic interactions when the fundamental axial periods migrate into the wave excitation range, potentially inducing significant hang-off loads3. When this interaction or coupling is known or shown to be insignificant, superposition of responses computed from independent lateral and axial dynamicanalyses is appropriate and efficient. However, if axial-lateral interactions cannot be discounted, filly coupled analyses become appropriate, even if only to confirm that coupling effects are insignificant.