报告题目：Grazing Induced Bifurcations: Innocent or Sinister?

报告人：Professor Marian Wiercigroch FRSE

报告人单位：Centre for Applied Dynamics Research

School of Engineering

University of Aberdeen, UK

报告时间：2018-09-01，上午09:00-12:00

报告地点：郑州大学数学与统计学院二楼金融实验室

 学术报告简介

Grazing Induced Bifurcations: Innocent or Sinister?

In this lecture I will examine nature of subtle phenomenon such grazing bifurcations occurring in non-smooth systems. I will start with linear oscillators undergoing impacts with secondary elastic supports, which have been studied experimentally and analytically for near-grazing conditions [1]. We discovered a narrow band of chaos close to the grazing condition and this phenomenon was observed experimentally for a range of system parameters. Through stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits, created at "invisible" grazing collide [2].

The experimentally observed bifurcations are explained theoretically using mapping solutions between locally smooth subspaces. Smooth as well as non-smooth bifurcations are observed, and the resulting bifurcations are often as an interplay between them. In order to understand the observed bifurcation scenarios, a global analysis has been undertaken to investigate the influence of stable and unstable orbits which are born in distant bifurcations but become important at the near-grazing conditions [3]. A good degree of correspondence between the experiment and theory fully justifies the adopted modelling approach. 

Similar phenomena were observed for a rotor system with bearing clearances, which was analysed numerically [4] and experimentally [5]. To gain further insight into the system dynamics we have used a path following method to unveil complex bifurcation structures often featuring dangerous co-existing attractors.

References

1. Ing, J., Pavlovskaia, E.E., Wiercigroch, M. and Banerjee, S. 2008 Philosophical Transactions of the Royal Society – Part A366, 679-704. Experimental study of impact oscillator with one sided elastic constraint.

2. Banerjee, S., Ing, J., Pavlovskaia, E., Wiercigroch, M. and Reddy, R. 2009 Physical Review E79, 037201. Invisible grazing and dangerous bifurcations in impacting systems.

3. Ing, J., Pavlovskaia, E., Wiercigroch, M. and Banerjee, S. 2010 International Journal of Bifurcation and Chaos20(11), 3801-3817. Complex dynamics of bilinear oscillator close to grazing.

4. Páez Chávez, J. and Wiercigroch, M. 2013Communications in Nonlinear Science and Numerical Simulation18, 2571–2580. Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model.

5. Páez Chávez, J., Vaziri Hamaneh, V. andWiercigroch, M.2015Journal of Sound and Vibration 334, 86-97. Modelling and experimental verification of an asymmetric Jeffcott rotor with radial clearance.

Marian Wiercigroch - Brief Bio 

Professor Marian Wiercigroch educated in Poland, US and UK holds a Sixth Century Chair and he is a founding director of the Centre for Applied Dynamics Research at the University of Aberdeen.

His area of research is theoretical and experimental nonlinear dynamics, which he applies to various engineering problems. Wiercigroch has published extensively (over 350 journal and conference papers) and sits on a dozen editorial boards of peer review journals. He is a joint Editor-In-Chief of International Journal of Mechanical Sciences and a frequent keynote and plenary speaker at major international conferences.

He is the inventor of new patented drilling technology called Resonance Enhanced Drilling and he has established in Aberdeen unique experimental laboratories allowing to investigate complex nonlinear dynamic interactions in mechanical systems.  

He has received many awards and distinctions including a Senior Fulbright Scholarship in 1994. In 2009 for his contribution to engineering and mathematics he was elected a Fellow of the Royal Society of Edinburgh, the Scotland national academy and in 2013 he was awarded an honorary doctorate, DSc honoris causa, by the Lodz University of Technology and  in 2017 he was granted a title of an Honorary Professor at the Perm National Research Polytechnic University.