Planar dynamics of inclined cables carrying moving oscillators

The dynamic analysis of small-sag inclined cables carrying an array of oscillators moving with arbitrarily varying velocities is addressed. An appropriate static condensation procedure which leads to a unique nonlinear integro-differential equation in the transverse displacement component of the cable is applied. Such equation turns out to be coupled with the set of ordinary differential equations governing the absolute displacements of the moving oscillators. In the context of the Galerkin method, the convergence of the conventional series expansion of cable response is improved by adding a correction term accounting for the “quasi-static” contribution of the truncated high-frequency modes.