scholarly journals Internal resonance in a parametrically excited two-degree-of-freedom system with nonlinear spring characteristics. (2nd report, On the combination type)

1986 ◽  
Vol 52 (474) ◽  
pp. 657-663
Author(s):  
Yukio ISHIDA ◽  
Toshio YAMAMOTO
Keyword(s):  
Internal Resonance ◽  
Degree Of Freedom ◽  
Parametrically Excited ◽  
Nonlinear Spring ◽  
Two Degree Of Freedom

Degenerate “Star” Bifurcations in a Twinkling Oscillator

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Normal Form ◽  
Multiple Equilibria ◽  
Degree Of Freedom ◽  
Negative Stiffness ◽  
Nonlinear Spring ◽  
Mass Chain ◽  
New Type ◽  
Two Degree Of Freedom

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.

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