A Frequency-Domain, Finite-Order Representation of a Catenary Riser’s Dominant Nonlinear Dynamics

Abstract

A numerical simulation and system identification approach to the dynamic equilibrium of a catenary riser has been developed. A finite DOF representation of the dominant dynamics is constructed using frequency domain identification by applying nonlinear signal theory techniques on response data series when exciting the structure with sinusoidal motions at the top. Data series are obtained through numerical integration of a finite differences simulation model on the basis of the six nonlinear partial differential equations describing the riser dynamics. Dynamic equilibrium is mathematically formulated by the very same equations that implicate both geometric and hydrodynamic nonlinearities; the latter are depicted by Morison’s formula. Thus, spatio-temporal series are generated for riser bending moments induced by sinusoidal heave motions of various amplitudes and frequencies. These data are consequently transformed to the frequency domain where complex Singular Value Decomposition is applied in order to derive the full nonlinear spectrum. The significant harmonics of the riser’s spectrum for the bending moment on the 2D plane of reference are demonstrated to be the three lower odd harmonics and a set of orthogonal modes for these three significant harmonics is derived. The methodology proposed is finally applied to a typical test case for validation.