A computer model for dynamically analyzing a marine drilling riser has been developed. The model predicts a time history of riser stresses, deflections, and lower ball joint angle. This approach is novel in that it includes both random wave and vessel motion models. The random wave model allows one to specify any wave spectrum, from which the model generates a synthetic wave by decomposing the spectrum. The vessel motion model ties directly to the wave model and requires specification of the characteristics of the vessel's station-keeping system (mooring or dynamic positioning) and the vessel's response amplitude operators in surge or sway. Results of dynamic analyses of drilling risers will be discussed for various water depths.
Marine drilling riser (see Fig. 1) stresses, deflections, and the lower ball joint angle can be predicted with either a static or a dynamic model. A static computer program, RISER (now commercially available on Control Data Corporation's Cybernet System), loads the riser with a static force derived by combining current and wave forces obtained from Morison's equation.
In most instances, a static riser analysis will produce reasonable engineering simulations of riser behavior. This occurs when the zone of hydrodynamic damping over the riser overwhelms the zone of excitation along the riser. Frequently, however, the combination of vessel motion, oscillatory wave effects, and possible excitation of the riser's dynamic modes often requires that a dynamic analysis be performed to more precisely predict riser behavior and the locations of critical stressing zones.
There are three basic types of dynamic analyses: a steady-state or frequency-domain analysis, a nondeterministic random vibration analysis, and a deterministic time history analysis. Burke (Ref. 2) presents a dynamic steady-state riser analysis procedure in which only steady-state wave loadings and vessel motion oscillation at the corresponding wave period are permitted. To account for the effect of current loading and mean vessel offset, Burke uses a static analysis. He then combined the dynamic steady-state analysis and the static analysis to obtain total stresses and deflections. Unfortunately, Morison's equation includes nonlinear terms which, in many cases, will not permit superposition of the static and steady-state analyses. Because of this, we believe that random wave and vessel response are not modeled accurately using Burke's approach. However, using only the dynamic steady-state analyses, Burke demonstrates that the dynamic behavior of the riser, caused primarily by vessel response to waves, is a significant design factor in all water depths. The present paper demonstrates the effect of both the random waves and the coupled vessel response.
The second approach to a dynamic analysis is the nondeterministic random vibration method as presented by Tucker and Murtha (Ref. 3). In this method, the random wave spectrum is input to the riser model, and the riser response is output in the form of a spectrum. They show that the response of a riser to random wave forces is highly dependent on the input wave energy spectrum.
