FREE-VIBRATION OF 2 COUPLED NONLINEAR OSCILLATORS

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 equati ons for a van der Pol oscillator coupled with a Duffing oscillator. Fo r the case of non-resonant oscillations, these equations are in standa rd normal form of a codimension two (Hopf-Hopf) bifurcation, which per mits a complete analysis to be performed. Three different types of asy mptotic states - corresponding to trivial, periodic and quasiperiodic motions of the original system - mare obtained and their stability is analyzed. Transitions between these different solutions are also ident ified and analyzed in terms of two appropriate parameters. Then, effec ts of a coupling, a detuning, a nonlinear stiffness and a damping para meter 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 dyna mical systems.