Abstract
This work explores complex dynamics of a new mass excited impact oscillator reported in Wiercigroch et al. (Nonlinear Dyn 99:323–339, 2020) both experimentally and numerically in the context of development of chaos theory and its applications. The parameters of the rig were characterised and are presented in the paper. To improve quality of the recorded phase portraits, a new technique for processing of the experimental data allowing to reduce the influence of noise and to obtain clear orbits especially for higher periods is proposed. A comparison with the previous studies on the base excited impact oscillator confirms that the rig is much more accurate as well as it has capability to generate a wide range of excitation patterns. It is demonstrated that a precise control of the excitation is achieved by changing the coil current. It is also shown that the rig is able to capture co-existent attractors and multi-stability by reproducing various predicted numerical responses, which has not been possible before. The results obtained using a simple impact oscillator model are in a good agreement with the experimental results, which indicates that the rig can be used for further fundamental studies of impact phenomena including grazing. It can also serve as a tool to study nonlinear control including bifurcation control and control of co-existing orbits.
Highlights
The impacting systems represent a field of research that is fundamentally important and it has a wide range of applications
Two cases are considered: in the first one, frequency bifurcation diagrams are obtained for different values of the excitation amplitudes and gaps, while in the second one the excitation amplitude is used as branching parameter
The detailed study of the excitation provided by the magnetic coil revealed a linear relationship between the applied current and the force acting on the mass in the considered parameters range
Summary
The impacting systems represent a field of research that is fundamentally important and it has a wide range of applications. Impacts introduce nonlinearities to those systems, which in turn may induce various behaviours ranging from periodic responses of high period to chaotic motions [27,28] On one hand, these new types of vibration can be highly undesired, for example in machining where imperfections are directly related to nonlinear phenomena [16,29]. A series of publications from the Centre of Applied Dynamics at Aberdeen presents the dynamics of a base excited experimental impact oscillator rig, with a free one-sided impact [46,47,48,49] and a pre-loaded impact [50] In these studies, various nonlinear phenomena were observed experimentally including chaos and periodic motions of high period, but a much wider range of responses were found numerically including co-existing of multiple attractors.
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