Abstract
In this paper, we study a model of a flexible hoisting system, in which external disturbances exerted on the boundary can induce large vibrations, and so damage to the performance of the system. The dynamics is described by a wave equation on a slow time-varying spatial domain with a small harmonic boundary excitation at one end of the cable, and a moving mass at the other end. Due to the slow variation of the cable length, a singular perturbation problem arises. By using an averaging method, and an interior layer analysis, many resonance manifolds are detected. Further, a three time-scales perturbation method is used to construct formal asymptotic approximations of the solutions. It turns out that for a given boundary disturbance frequency, many oscillation modes jump up from order ε amplitudes to order ε amplitudes, where ε is a small parameter with 0
| Original language | English |
|---|---|
| Pages (from-to) | 44-62 |
| Number of pages | 19 |
| Journal | Applied Mathematical Modelling |
| Volume | 111 |
| DOIs | |
| Publication status | Published - 2022 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- Resonance
- Boundary excitation
- Time-varying length
- singular perturbation
- Averaging