Reduced-order, nonlinear approximation of catenary riser dynamics using frequency domain identification

Abstract

This paper demonstrates an approximation to the numerical solution of the dynamic equilibrium of a catenary riser. The approximant is obtained in the frequency domain when the structure is excited by motions applied at the top. The dynamic equilibrium is formulated mathematically through six nonlinear partial differential equations which involve both geometric and hydrodynamic nonlinearities. The latter are represented by the Morison’s formula. The numerical solution of the six nonlinear differential equations is used to generate spatio-temporal data series for riser bending moments induced by sinusoidal heave motions of various amplitudes and frequencies. The data series are transformed to the frequency domain where a complex singular value decomposition scheme is applied in order to reconstruct the full nonlinear spectrum. The significant harmonics of the riser’s spectrum are then identified as the three lower odd harmonics. The method finally provides a set of orthogonal modes for all significant harmonics; that is, the fundamental, the third and the fifth harmonic of the bending moment in the 2D plane of reference. The nonlinear, frequency-domain modal decomposition proposed is also examined in a typical test case.