Wagg, David James; (1999) Vibro-impact dynamics of engineering systems. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Many problems in engineering involve systems with vibrating components which can impact with a rigid boundary. The aim of this research is to improve our understanding of the dynamics associated with such vibro-impact systems, thus enabling more accurate mathematical modelling of associated engineering problems. Initially we consider a single degree of freedom impact oscillator system. Such systems have been widely studied and are discussed here in terms of fundamental impacting motions and nonlinear mappings. The bifurcational behaviour of the system is studied and compared to results from an experimental system. In particular we consider the codimension two bifurcations which occur and demonstrate how these events can be used to maintain periodic motion of the beam during parameter variation. We then consider developing a structured approach for parameter estimation using experimentally recorded data. An energy analysis for single degree of freedom systems is presented. This is used to develop a method for estimating the coefficient of restitution and damping parameters using a time series obtained from a physical system. Using a purpose built experimental impact load cell we estimate impact forces for an impacting beam system. We discuss the analysis of impulse spike data, and show how system dynamics can be reconstructed using interspike intervals. We then consider the dynamics of multi-degree of freedom impact oscillators, including sticking and chatter motions, using a two degree of freedom lumped mass model as an example. The energy analysis developed for the single degree of freedom system is extended to multi-degree of freedom systems and the effect of energy transfer between modes and reduction in coefficient of restitution is discussed. Finally we consider how such work may be applied to continuous systems such as the cantilever beam using a Galerkin approach. We compare these results qualitatively with experimental data from flexible vibro-impacting beams.

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