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 p eriodic external excitation is analyzed. Due to the time-varying lengt h of the vertical cable the natural frequencies of the system vary slo wly, and a transient resonance may occur when one of the frequencies c oincides with the frequency of an external excitation at some critical time. A simplified model of the system with proportional damping is p roposed. This model is analyzed by using a combined perturbation and n umerical technique. The method of multiple scales is used to formulate a uniformly valid perturbation expansion for the response near the re sonance, and a system of first order ordinary differential equations f or the slowly varying amplitude and phase of the response results. Thi s system is integrated numerically on a slow time scale. A model examp le is discussed, and the behavior of the essential dynamic properties of the system during the transition through resonance is examined. (C) 1997 Academic Press Limited.