Travelling load response of an axially moving string

Abstract The classical moving load problem in which a mass traverses an elastic structure is extended to systems in which the guideway also has prescribed axial motion. A monocable ropeway, such as a tramway or ski lift, is an example of such a traveling structure-traveling load system, and it is modeled herein as an axially moving string that transports an attached discrete mass between two supports. The Green's function methods for the two constituent systems, the particle and the uniform traveling string, are combined to derive a Volterra integral equation with delay that governs the interaction force in the coupled system. The calculated response of the traveling string-particle system to arbitrary initial conditions and external excitation is compared to that predicted by the derived asymptotic solution for vanishing discrete mass. Repeated scattering by the particle of transverse waves in the string dominates the motion. Transient vibration as the particle is transported between the supports is maximized at a transport speed that can be substantially lower than the critical speed of divergence instability for the uniform traveling string. Agreement between responses measured in the laboratory and those predicted by the traveling structure-traveling load theory supports the analysis.