Dynamics of Suspended Cables Crossed by Moving Oscillators

In-plane vibrations of flat-sag suspended cables carrying a stream of oscillators moving with arbitrary time-law are analyzed. The equations of motion of the coupled cable-moving oscillators system are derived. In particular, neglecting the longitudinal inertia forces and applying a standard condensation procedure, the motion equations of the cable are reduced to a unique nonlinear integro-differential equation in the vertical cable vibrations which is coupled to the ordinary differential equations ruling the response of the moving oscillators in terms of absolute displacements. An approximate solution is pursued by the Galerkin method assuming an improved series representation of vertical cable displacement recently proposed by the authors in order to accurately describe the abrupt changes of cable profile at the contact points with the moving oscillators.