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Bifurcation in a parametrically excited two-degree-of-freedom nonlinear oscillating system with 1∶2 internal resonance
- Source :
- Applied Mathematics and Mechanics. 20:350-359
- Publication Year :
- 1999
- Publisher :
- Springer Science and Business Media LLC, 1999.
-
Abstract
- The nonlinear response of a two-degree-of-freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first-order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steadystate solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.
- Subjects :
- Applied Mathematics
Mechanical Engineering
Saddle-node bifurcation
Dynamical system
Nonlinear Sciences::Chaotic Dynamics
Nonlinear system
Pitchfork bifurcation
Classical mechanics
Mechanics of Materials
Ordinary differential equation
Parametric oscillator
Bifurcation
Mathematics
Multiple-scale analysis
Subjects
Details
- ISSN :
- 15732754 and 02534827
- Volume :
- 20
- Database :
- OpenAIRE
- Journal :
- Applied Mathematics and Mechanics
- Accession number :
- edsair.doi...........6ad47b94efc10c6634362348ef00f219