Nonlinear vibration modes of an offshore articulated tower

Compliant structures, due to their low stiffness and hostile environmental loads, may present large displacements and rotations, leading to significant nonlinear effects. This work applies the theory of nonlinear normal modes to investigate the nonlinear vibrations of a discrete two-degree-of-freedom conceptual model of an offshore compliant articulated tower. The effects of buoyancy, added mass, ocean currents and waves are considered in the analysis. The elastic restoring forces are modeled, based on Augusti's model, using two orthogonal rotational springs. The invariant-manifold approach is then applied to the equations of motion, and the resulting equations are solved through an asymptotic expansion. The derived nonlinear normal modes are then used to reduce the problem to a single degree-of-freedom nonlinear oscillator in each mode. The stability of the solution is investigated through Floquet theory and Mathieu charts. Multiplicity of stable and unstable modes is detected using Poincaré sections. Similar and non-similar modes are also identified. The results of the reduced order model are compared to the numerical solutions of the original equations of motion. The favorable comparisons between both solutions confirm that nonlinear normal modes are a good alternative for the nonlinear analysis of an articulated tower and similar offshore structures.