On the Period-Doubling Bifurcations in the Duffing’s Oscillator With Negative Linear Stiffness

[+] Author and Article Information
K. R. Asfar, K. K. Masoud

Department of Mechanical Engineering, Jordan University of Science and Technology, Irbid-Jordan

J. Vib. Acoust 114(4), 489-494 (Oct 01, 1992) (6 pages) doi:10.1115/1.2930289 History: Received December 01, 1990; Online June 17, 2008


The phenomenon of period-doubling bifurcations in the Duffing’s oscillator with negative linear stiffness is investigated with the aid of approximate analytical methods and computer simulation. Making use of a Hill’s type variational equation together with the ideas drawn out from Floquet theory, it is found that a particular type of subharmonic instability is the one that is responsible for the occurrence of period-doublings in this system. This fact is confirmed by the good agreement between the true critical forcing frequency at which bifurcations are first observed, and the one obtained theoretically. Finally, a threshold criterion for the onset of period-doublings is also proposed and compared with computer simulation results.

Copyright © 1992 by The American Society of Mechanical Engineers
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