A method for the dynamic analysis of suspended cables carrying moving masses

An efficient procedure for analyzing in-plane vibrations of suspended cables carrying an array of moving masses is presented. The cable/mass system is modelled by properly including both the geometrical nonlinearities and the interaction forces due to the convective acceleration of the moving masses. The nonlinear partial differential equations governing in-plane vibrations are derived through the extended Hamilton's principle and then solved approximately by the Galerkin method adopting appropriate basis functions. Following the well-known "mode-acceleration" method, the convergence of the series expansion in terms of the selected basis functions is improved through the introduction of the so-called "quasi-static" solution. Numerical results demonstrate that, despite the basis functions are continuous, the improved series enables to capture with very few terms the abrupt changes of cable profile at the contact points between the cable and the masses.