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### Talk on February 11, 2002, 3pm at room 415

Gabor Csernak
Budapest University of Technology and Economics

Department of Applied Mechanics

H-1521 Budapest, Muegyetem rkp. 5.

csernak@mm.bme.hu

## Transient chaotic phenomena in engineering problems

There are many examples in engineering vibration problems where chaotic
oscillations may occur. These oscillations often disappear suddenly --
this phenomenon is referred to as
transient or metastable chaos. It is usually considered by engineers as a
regular motion since it may look like the conventional transient behaviour
when a machine starts its operation. However, this transient behaviour cannot
be characterized by conventional damping factors since the transient chaotic
oscillation does not produce an exponential decay in amplitudes, it rather
disappears unexpectedly. Actually, similar initial operation of a machine may
produce very different time periods of transient oscillations. The duration
of these oscillations -- which can be an important parameter for
the design work -- varies stochastically, so the estimation of the life
expectancy of the transient motion needs extensive statistical
analysis.
In the presentation some engineering vibration problems will be introduced, in which
transient chaotic phenomena may occur. The first one is the case of metal cutting,
while the other ones are the digital control of stick-and-slip motion, and the so-called
shimmy motion of towed wheels.

In some cases, the life expectancy of the transient chaotic behaviour was calculated,
using the methods based on the Perron-Frobenius theory. We applied a new
approach to perform these calculations. The results obtained by the different methods will
also be introduced in the talk.

Contact: Udo Schwarz