We have studied a nonlinear spring-mass chain loaded by a quasistatic pull. The spring forces are assumed to be cubic with intervals of negative stiffness. Depending on the parameters, the system has multiple equilibria. The normal form and the bifurcation behaviors for the single- and two-degree-of-freedom systems are studied in detail. A new type of bifurcation, which we refer to as a star bifurcation, has been observed for the symmetric two-degree-of-freedom system. This bifurcation is of codimension-four for the undamped case and codimension-three or two for the damped case, depending on the form of the damping.
Degenerate “Star” Bifurcations in a Twinkling Oscillator
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 22, 2013; final manuscript received August 4, 2013; published online December 9, 2013. Assoc. Editor: Brian P. Mann.
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Panigrahi, S. R., Feeny, B. F., and Diaz, A. R. (December 9, 2013). "Degenerate “Star” Bifurcations in a Twinkling Oscillator." ASME. J. Vib. Acoust. April 2014; 136(2): 021004. https://doi.org/10.1115/1.4025442
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