A semi-analytical method is employed to investigate stability of the nonlinear response of an articulated tower. Local and global bifurcations determine the possible existence of complex nonlinear and chaotic motions which cannot be obtained through evaluation of an equivalent linearized system.
Complex nonlinear and chaotic responses have been recently observed in various models of articulated towers and other compliant ocean systems (eg. Thompson et aI., 1984; Liaw, 1988). Similar behavior has been found in roll response of ships and semisubmersibles where the restoring moment was modeled b) a quintic polynomial (Nayfeh and Khdeir, 1986; Witz et aI., 1989). Articulated towers are surface piercing columns pinned to the sea floor which serve as mooring loading terminals for oil tankers. They are characterized by a nonlinear restoring moment and a nonlinear coupled hydrodynamic exciting moment. The restoring moment of the articulated tower is that of a forced plane pendulum and is generated by an internal excess buoyancy mechanism. The exciting moment includes a coupled wavestructure viscous drag component and a wave induced inertial moment. The drag component consists of parametric and quadratic damping, a bias and harmonic forcing. The forced pendulum has been extensively investigated and complex nonlinear behavior such as coexistence of attractors, symmetry breaking, period doubling and internlittency have been found experimentally, numerically and analytically (D"Humiers et aI., 1982; Miles, 1988). Furthermore, global asymptotic criteria for the existence of chaotic response have been derived for the pendulum and for a Josephson junction circuit (Salam and Sastry, 1985) modeled as a forced and biased pendulum. However, unlike the unperturbed pendulum which has a pair of homoclinic orbits separating the domain of response into two disjoint parts of bounded and unbounded solutions, the articulated tower belongs to a family of oscillators which have a unique equilibrium position.