Nonlinear dynamics of a submerged floating moored structure by incremental harmonic balance method with FFT

A submerged floating moored structure has a great potential in ocean engineering applications. The nonlinear dynamics of a submerged floating moored structure subjected to vertical excitation with possible slackness in the mooing system are investigated by incremental harmonic balance (IHB) method. Heaviside step function is introduced to describe the nonlinearity in axial stiffness arising from loss of mooring tension. The dimensionless governing equation is derived, and three parameters, frequency ratio η, damping ratio ζ and dimensionless net buoyancy W, are found to be independent. Due to the fact that the restoring force term is function of the unknown displacement and could barely be expressed in an explicit form of time, a fast Fourier transformation (FFT) is implemented in IHB method to simplify the Galerkin average procedure. Both stable and unstable solutions and both period-1 and bifurcated solutions are obtained by IHB method. The stability of the periodic solutions is investigated by Floquet theory. Parameter study is carried out. Results indicate that the system nonlinearity becomes stronger as dimensionless the net buoyancy W and damping ratio ζ decrease. A path to chaotic motions though a series of period doubling bifurcations is found. Multiple solutions are observed, and the domains of attraction are investigated by interpolated cell mapping (ICM) technique.