The passage through resonance in a catenary-vertical cable hoisting system with slowly varying length

A passage through resonance in a catenary-vertical cable system with periodic external excitation is analyzed. Due to the time-varying length of the vertical cable the natural frequencies of the system vary slowly, and a transient resonance may occur when one of the frequencies coincides with the frequency of an external excitation at some critical time. A simplified model of the system with proportional damping is proposed. This model is analyzed by using a combined perturbation and numerical technique. The method of multiple scales is used to formulate a uniformly valid perturbation expansion for the response near the resonance, and a system of first order ordinary differential equations for the slowly varying amplitude and phase of the response results. This system is integrated numerically on a slow time scale. A model example is discussed, and the behavior of the essential dynamic properties of the system during the transition through resonance is examined. © 1997 Academic Press Limited.