Nonlinear periodic response analysis of mooring cables using harmonic balance method

Mooring cables are critical components of ocean renewable energy systems including offshore floating wind turbines and wave energy converters. Mooring cable dynamics is strongly nonlinear resulting from the geometric effect, hydrodynamic loads and probably seabed interactions. Time-domain methods are commonly used for numerical simulation. This study formulates a nonlinear frequency domain multi-harmonic balance method for efficient analysis of a mooring cable subjected to periodic fairlead motions. The periodic responses are of particular interest to investigate the mooring effect on the platform. In the formulation, the governing equations of the three-dimensional cable motions are spatially discretized using the finite difference method; the nonlinear ordinary differential equations are subsequently transformed into the frequency domain by expanding both the structural responses and the nonlinear nodal forces using truncated Fourier series, leading to a set of nonlinear algebraic equations of the Fourier coefficients. The equations are eventually solved using Newton's method where the alternating frequency/time domain method is used to handle the nonlinearity effect. The presented method is then compared to a time-domain method by numerical studies of a mooring cable. The results show that the method is of comparable accuracy as the time-domain method while it is generally more efficient. The proposed method shows promising results even when the cable tension becomes non-positive for a period of time during the cable motion, which is a known ill-posed problem for time-domain methods.