Nonlinear in-plane vibrations of inclined cables carrying moving oscillators

In-plane dynamics of small-sag inclined cables carrying a stream of oscillators moving with arbitrarily varying velocity is addressed. A condensed model of the coupled cablemoving oscillators system is derived by referring cable vibrations to a local Cartesian coordinate system. Specifically, relying on the negligible influence of the inertia forces along the cable chord and assuming a quasi-static stretching during the motion, an appropriate static condensation procedure is applied which enables to account for the chordwise components of the interaction forces between the cable and the moving subsystems . Thus, the governing equations are reduced to a unique nonlinear integrodifferential equation in the transverse displacement of the cable coupled to the ordinary differential equations ruling the response of the moving oscillators in terms of absolute displacements. The condensed model is discretized by the Galerkin method assuming an improved series expansion of cable response able to accurately reproduce the abrupt changes of cable profile at the contact points with the moving oscillators. A numerical application is presented to validate the proposed condensed model of the inclined cable under moving oscillators as well as the improved series representation of cable response.