On modelling and linear vibrations of arbitrarily sagged inclined cables in a quiescent viscous fluid

A theory of free linear vibrations of arbitrarily sagged inclined cables in a viscous fluid is presented in the framework of the heavy fluid loading concept. The static equilibrium shape of the cable is found by using the model of inextensible catenary and the validity ranges of this approximation are assessed. The dynamics of the viscous fluid is described by the linearised Navier–Stokes equations and their solution is pursued analytically by formulating the fluid field variables via potential functions. The vibration problem of a submerged cable is solved by Galerkin's method and the modal added mass and modal viscous damping coefficients are calculated. As a prerequisite for this analysis, the free vibrations of a cable in vacuum are addressed and a very good agreement with known results is observed. The physical interpretation of the dependence of modal added mass and modal damping coefficients on the ‘design variables’ for a fluid-loaded cable is given and the possible extensions of the suggested theory to capture weakly nonlinear effects are highlighted.