Abstract

KACZMARCZYK, Stefan. Transient resonance in a hoisting cable system with a periodic excitation. R&D j. (Matieland, Online) [online]. 1997, vol.13, pp.31-40. ISSN 2309-8988.

The non-stationary oscillations of slowly varying oscillatory distributed one-dimensional systems can be analysed using a combined perturbation and numerical technique. This approach is used to investigate a passage through resonance in a hoisting cable system. Due to the time-varying length of the 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. The method of multiple scales is used to formulate a uniformly valid perturbation expansion for the response near the resonance. A system of first order ordinary differential equations for the slowly varying amplitude and phase of the response results. This system can be easily integrated numerically on a slow time scale. A model example is discussed, and it is shown that the amplitude of the oscillations remains large after the passage through resonance.

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