Modeling and vibratory characteristics of a mass-carrying cable system with multiple pulley supports in span range

A theoretical dynamic model of a multi-segment mass-carrying cable system with multiple pulley supports is derived. Unlike many existing analytical cable models, the relative movement between the cable and pulley supports is considered here. The cable is modeled as a combination of a number of segments connecting the mass and the pulley supports. The Hamilton principle is used to account for the relative moving boundaries between the cable and the pulley supports. From the continuity conditions, boundary conditions and force equilibrium conditions, the non-dimensional unforced undamped characteristic equation is obtained. The natural vibratory characteristics for this kind of cable are also determined. The effects of the mass ratio and sag-to-span ratio on the frequency spectra are studied. The Pareto chart of the fundamental frequency of the multi-segment cable is examined. The results show that the frequencies are either sensitive to or independent of non-dimensional parameters in certain parameter ranges. Veering phenomena also appear between the frequencies of two approaching modes.