flexible marine riser; large deformations; deep water; lumped mass; Kane's method; waves; current
The equations of the three dimensional motion of a marine riser undergoing large elastic deformations are formulated using Kane's formalism. The riser is modeled using lumped masses connected by extensional and rotational springs including structural damping. Surface waves are described by Stokes' second-order wave theory. Fluid-structure coupling is achieved by application of the hydrodynamic loads via Morison's equation and added-mass coefficients using the instantaneous relative velocities and accelerations between the fluid field and the riser segments. In the same way, a model for incorporating the effects of vortex-induced lift forces is included. The effect of internal flow is included in the model. The detailed algorithm is presented and the equations are solved using a robust implementation of the Runge-Kutta method provided in MATLAB. The mathematical model and associated algorithm are validated by comparing the steady-state equilibrium configuration of the riser with special cases of an elastic catenary mooring line and large deflection statics of a cantilever beam. The results of sample simulations are presented.
Multibody System Dynamics10, no. 4 (2003): 393–423.