Free vibration of two coupled nonlinear oscillators

✍ Scribed by S. Natsiavas

• Publisher: Springer Netherlands
• Year: 1994
• Tongue: English
• Weight: 799 KB
• Volume: 6
• Category: Article
• ISSN: 0924-090X
• DOI: 10.1007/bf00045433

✦ Synopsis

An analytical investigation is carried out on the free vibration of a two degree of freedom weakly nonlinear oscillator. Namely, the method of multiple time scales is first applied in deriving modulation equations for a van der Pol oscillator coupled with a Duffing oscillator. For the case of non-resonant oscillations, these equations are in standard normal form of a codimension two (Hopf-Hopf) bifurcation, which permits a complete analysis to be performed. Three different types of asymptotic states -corresponding to trivial, periodic and quasiperiodic motions of the original systemare obtained and their stability is analyzed. Transitions between these different solutions are also identified and analyzed in terms of two appropriate parameters, Then, effects of a coupling, a detuning, a nonlinear stiffness and a damping parameter are investigated numerically in a systematic manner. The results are interpreted in terms of classical engineering terminology and are related to some relatively new findings in the area of nonlinear dynamical systems.