Karpodinis, George; (2002) The dynamic response of an impacting driven beam: Experiments and mathematical model. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Systems consisting of vibrating components that repeatedly impact with rigid boundaries are in the heart of engineering. The aim of this research is to improve our understanding of such vibro-impact systems and thus to enable more accurate monitoring, interpretation and modelling of their behaviour. We use a mechanical impacting oscillator as our source of experimental data. An impact load cell is used to measure the forces exerted upon impact. These data are analysed to assess the suitability of an instantaneous impact assumption for the impacts. The problem is quantified and the suitability of the model is proved. The single degree of freedom model, combined with an instantaneous impact rule, is then used to compare and verify our experimentally obtained results. Using thresholded measurements from the impact load cell, we show that the correlation dimension can be estimated. Using interspike intervals from the vibro-impacting motion, we successfully reconstruct the dynamics of the system for different kinds of periodic behaviour. By simulating the data acquisition process, we also show that the results obtained by thresholding the measurements are qualitatively similar to results obtained in 'noisy' environments. A way to remotely extract the same information from the vibro-impact system is presented. We investigate whether the sound of the impacts carries enough information to reconstruct the dynamics. We show that this is possible by reconstructing two types of behaviour. The results show great similarity to those obtained from the impulse spike data. Control of the vibro-impacting behaviour is attempted using Pyragas's method. Perturbations are successfully used to force the system into motion of a particular period. We investigate how different strengths of control might assist in overcoming difficulties in stabilising certain orbits. Finally, we show that using control, the behaviour of the system can be swiftly altered at will and migrate between different orbits.

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