Parametric instabilities in the out-of-plane dynamics of catenary-shaped slender structures transporting fluids

The present study investigates the out-of-plane buckling behaviour of catenaries conveying fluids and subjected to end-imposed axial excitations. The mathematical formulation is generic with no restrictions in the amount of sag in the plane of reference. The theoretical model is treated using the Galerkin expansion and employing the actual mode shapes. It is shown that under a parametric excitation the physical model behaves as a multiple-degree-of-freedom system. The novelty of the present study is that it finds the equivalent system that governs the dynamics of the catenary, while in addition it accounts for the internal flow effects which arise from `compressive loading' and Coriolis forces. The stimulation of potential instabilities is investigated using the Floquet theory and the method of multiple scales.