ISSN:
1662-7482
Source:
Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
We demonstrate a method for tracking the onset of oscillations (Hopf bifurcation) in nonlineardynamical systems. Our method does not require a mathematical model of the dynamical systembut instead relies on feedback controllability. This makes the approach potentially applicable in anexperiment. The main advantage of our method is that it allows one to vary parameters directly alongthe stability boundary. In other words, there is no need to observe the transient oscillations of thedynamical system for a long time to determine their decay or growth. Moreover, the procedure automaticallytracks the change of the critical frequency along the boundary and is able to continue theHopf bifurcation curve into parameter regions where other modes are unstable.We illustrate the basicideas with a numerical realization of the classical autonomous dry friction oscillator
Type of Medium:
Electronic Resource
URL:
http://www.tib-hannover.de/fulltexts/2011/0528/01/39/transtech_doi~10.4028%252Fwww.scientific.net%252FAMM.5-6.417.pdf
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