Dynamic Response of Lazy-S Risers in Random Sea
Authors: Zare K. 
Published: October 2008

ABSTRACT
The response behaviour of lazy-S risers to dynamic forces in random sea environment is investigated. The dynamic response is measured about the mean static equilibrium position of the hanging riser under its submerged self weight and tension, which is determined by a separate finitedifference analysis. For the dynamic analysis, the hanging riser between the floater end and mid arch buoy is idealized as an assemblage of tensioned beam elements and the response is obtained by a simulation procedure using step by step time integration of the equations of motion. The dynamic forces considered are those produced by random wave forces together with steady current and consequent top vessel motion. The time history of the random top vessel motion is simulated with the help of the response amplitude operator of the top vessel and a wave superposition technique. The randomresponse of the riser is analysed for a number of cases to investigate its parametric behaviour and the statistics of response.

INTRODUCTION
The design of offshore facilities requires a realistic prediction of the stress and displacement response of the system under loading induced by random wave field. Most widely used spectral analysis for this purpose holds good when the inertial component of wave loading dominates. When the non-linear drag component in the wave loading is significant, as in the case of marine risers, the probabilistic description of the response is better achieved by extensivesimulation studies in which the response time histories are generated for a set of simulated random waves corresponding to a given sea state.
The dynamic response of straight marine risers to random sea environment has been obtained by many investigators. A few of them are cited in ref. (1-5). Two types of solutions are reported in these literature namely, frequency domain and time domain. Frequency domain methods linearized the drag term in the hydrodynamic loading and used spectral analysis to obtain mean square response. These solutions considered random wave forces and deterministic current, but no top vessel motion. Time domain methods were essentially based on simulation procedure in which time histories of hydrodynamic loading and top vessel motions (whenever considered) were generated for a given sea spectrum.
For flexible risers, the studies on the response due to random waves are meager. In particular, there is a lack of information in the literature regarding the statistics and randomnature of its response. The flexible risers (of free hanging type, 'lazy-s' or steep-s' configurations) are simplest and most economicalmeans of linking subsea equipment and floating facilities. They are becoming increasingly popular in offshore industry. In this paper, theresponse of the first suspended portion of the "Lazy-S" risers to random sea states is studied with the following objectives in view:topresent a time domain simulation analysis of flexible risers to random wave, current and instantaneous vessel motion;to study the random dynamic response behavior of the riser under different parametric variations;to estimate a relationship between the RMS and mean peak response for flexible risers under random wave environment.