Compensation of top horizontal displacements of a riser

The nonlinear dynamic problem of catenary risers is solved by means of the rigid finite element method. The method enables us to model slender systems such as lines, cables and risers undergoing large base motions. The formulation allows elimination of large values of stiffness coefficients: shear, longitudinal and torsional (dependent on permissibility of the system analyzed). The analysis presented in the paper is concerned with the dynamics of a riser initially bent and undergoing heave excitation. Comparison of the results with those obtained using the finite difference and finite element methods shows good compatibility and indicates the correctness of the models obtained by means of the rigid finite element method. Numerical effectiveness of the method enables it to be applied in solving the dynamic optimization problem. The problem described is the compensation of the horizontal vibrations of the vessel or a platform by vertical displacements of the upper end of the riser. Bending moments which arise during the motion of a platform or a vessel can seriously influence and in some cases damage the structure. Thus the aim of the optimization is to ensure that the maximum bending moment at a given point does not exceed its static counterpart. The results of numerical simulations show that the systems enabling heave compensation can be used to minimize the difference between the bending moment caused by displacements of the platform or a vessel and the static moment.