Publications [#282359] of Lawrence N. Virgin
- Virgin, LN; Wiebe, R, On damping in the vicinity of critical points.,
Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 371 no. 1993
pp. 20120426, ISSN 1364-503X , [doi]
(last updated on 2019/09/21)
The effect of damping on the behaviour of oscillations in the vicinity of bifurcations of nonlinear dynamical systems is investigated. Here, our primary focus is single degree-of-freedom conservative systems to which a small linear viscous energy dissipation has been added. Oscillators with saddle-node, pitchfork and transcritical bifurcations are shown analytically to exhibit several interesting characteristics in the free decay response near a bifurcation. A simple mechanical oscillator with a transcritical bifurcation is used to experimentally verify the analytical results. A transcritical bifurcation was selected because it may be used to represent generic bifurcation behaviour. It is shown that the damping ratio can be used to predict a change in the stability with respect to changing system parameters.