Second-order nonlinear dynamics of catenary pipelines: A frequency domain approach

• The double frequency nonlinear dynamic behavior of catenary pipelines is investigated.
• The original nonlinear system is treated using a perturbation technique.
• The seafloor interaction phenomenon is approximated through a Taylor series expansion.
• The discrete mathematical models are solved numerically using a centered difference scheme.
• The calculations demonstrate the significant contribution of the second-order components.

It is the purpose of the study to investigate the nonlinear dynamics of catenary shaped pipelines using a frequency domain technique. The study emphasizes on marine applications modeling the structure as a top tensioned riser with constant physical and mechanical properties. The original nonlinear system is treated using expansions of the dynamic components in perturbation series. The employed method results in discrete systems which can be treated separately and successively. It is shown that the mechanism that excites second-order effects relies on the quadratic nonlinearities due to the first-order components. The study is extended to capture the effects due to the interaction with the seafloor. To this end the boundary conditions which originally correspond to a pinned bottom-end point are expanded using a Taylor series around an average location. Following this approach it is shown that the associated phenomenon is itself nonlinear regardless the behavior of the soil.The proposed frequency domain approach was inspired by the solution methods employed in hydrodynamic boundary value problems which assume a perturbation series expansion for the velocity potential. The equivalent of the Taylor series approximation of the lower end boundary condition in the present structural model is the Taylor expansion of the free surface boundary conditions around an average, namely the undisturbed free surface.