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TUL - Division of Dynamics

Dane Kontaktowe / Contact Data



MME updated - May 2017

See Journal subpage: MME


MME updated - March 2017

See Journal subpage: MME


MME updated - January 2017

See Journal subpage: MME


MME updated - September 2016

New articles has been added to our Journal, April - Mechanics and Mechanical Engineering. See Journal subpage: MME

MME updated - June 2016

New articles has been added to our Journal, April - Mechanics and Mechanical Engineering. See Journal subpage: MME

MME updated - May 2016

New articles has been added to our Journal, April - Mechanics and Mechanical Engineering. See Journal subpage: MME


MME updated - March 2016

New articles has been added to our Journal, March - Mechanics and Mechanical Engineering. See Journal subpage: MME


Seminar by Patrycja Jaros

We invite all to the seminar by Patrycja Jaros: Solitary states in Kuramoto model with inertia (20 mins) which will be held in 2M221 at Friday, January 29, 2016, 10:00.


Seminar by Prof. Marian Wiercigroch

We warmly invite everyone to the seminar by Prof. Marian Wiercigroch from University of Aberdeen: Grazing Induced Bifurcations: Innocent or Dangerous? which will be held in 2M221 at January 26, 2016, 12:15.

Professor Wiercigroch comes from Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, UK. His abstract follows:

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 A 366, 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 E 79, 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 Chaos 20(11), 3801-3817. Complex dynamics of bilinear oscillator close to grazing.
4. Páez Chávez, J. and Wiercigroch, M. 2013 Communications in Nonlinear Science and Numerical Simulation 18, 2571–2580. Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model.
5. Páez Chávez, J., Vaziri Hamaneh, V. and Wiercigroch, M. 2015 Journal of Sound and Vibration 334, 86-97. Modelling and experimental verification of an asymmetric Jeffcott rotor with radial clearance.



MME updated - December 2015

New articles has been added to our Journal, December - Mechanics and Mechanical Engneering. See the Articles subpage: MME


Katedra Dynamiki Maszyn - Division of Dynamics

90-924 Łódź, ul. Stefanowskiego 1/15
K-13, bud. A22
Poland
tel.: +48 42 631 2231; +48 42 631 2430
Fax: +48 42 631 2702
e-mail: k-13@adm.p.lodz.pl;  tomaszka@p.lodz.pl










Entry date: 2015-07-24
Modified: 2017-06-22
Entered by: J Wojewoda