Three dimensional nonlinear dynamics of submerged, extensible catenary pipes conveying fluid and subjected to end-imposed excitations

The complete 3D nonlinear dynamic problem of an extensible, submerged catenary pipe conveying fluid is considered. For describing the dynamics of the system, the Newtonian derivation procedure is followed. The flow inside the pipe is considered inviscid, irrotational and incompressible with constant velocity along the complete length of the pipe. The hydrodynamic effects are taken into account through the nonlinear drag forces and the added inertia due to the hydrodynamic mass. Following the Newtonian derivation, the dynamics of the pipe element and the fluid element are considered separately and the final governing set is derived combining the equations of inertia equilibrium. The system is solved using an efficient, second-order accurate, finite differences numerical scheme. The effect of the steady flow inside the pipe on both the in-plane and the out-of-plane vibrations is assessed with the aid of numerical simulations using as a model a relatively small-sag submerged catenary. The output signals of the time varying components that govern the dynamics of the pipe, have been properly processed to assess the effect of the internal flow on both the in-plane and the out-of-plane vibrations.