Hydroelasticity of the Kirchhoff rod: Buckling phenomena

We consider the nonlinear coupled hydroelastic problem of a general curved and twisted flexible slender structure (i.e, flexible riser, cable system, fish-farm net system, towed arrays, etc.) embedded in a nonuniform flow fie ld such as the ocean environment; the flow direction is arbitrary, relative to the axis of the slender structure. The motion of the elastic structure is coupled with the hydrodynamic loads acting on the slender structure by t he ambient flow field. An important input for such hydroelastic problems is the computation of the hydrodynamic loading per unit length experienced by the slender body. A rigorously derived improvement for the inertial loadin g per unit length over the commonly used Morison-type semi-empirical force (originally obtained for straight long structures in a uniform stream) is u sed. The structure is also allowed to undergo small (yet finite) deflection s from its original reference central-line, due to a particular model of in trinsic elasticity governed by a corresponding nonlinear PDE, which corresp onds to the well-known Kirchhoff rod elastic model. The system of coupled h ydroelastic equations is investigated in order to derive analytically the i nfluence of the hydrodynamic loading in a uniform stationary stream on the nonlinear stability of the straight rod. It is found that the presence of a n ambient stationary stream decreases the critical parameters (critical twi st) of the buckling phenomenon which is known to exist for the same rod whe n placed in a vacuum. Also revealed is a new type of stability loss, which is affected by viscous effects. (C) 2000 Academic Press.