Forcing induced asymmetry on dynamical systems with cubic non-linearities

The present work investigates the dynamics of a class of two-degree-of-free dom oscillators with cubic non-linearity in the restoring forces. These osc illators are under the action of an external load including constant and ha rmonic components. Initially, a perturbation analysis is applied to the equ ations of motion, demonstrating the effect of the asymmetry induced by the constant loading component on the classical 1:1 and 1:3 internal resonances , as well as on the possibility of the appearance of a first order 1:2 inte rnal resonance. Next, sets of slow-flow equations governing the amplitudes and phases of vibration are derived for the special case of no internal res onance and for the most complicated case corresponding to 1:1 internal reso nance. The analytical findings are then complemented by numerical results, obtained by examining the dynamics of a two-degree-of-freedom mechanical sy stem. First, the effect of certain system parameters on the existence and s tability of constant and periodic solutions of the slow-flow equations is i llustrated by presenting a sequence of response diagrams. Finally, the dyna mics of the system used as an example is investigated further by direct int egration of the slow-flow equations. This shows the existence of a period-d oubling sequence culminating into a continual interchange between quasiperi odic and chaotic response. It also demonstrates a new transition scenario f rom phase-locked to phase-entrained and drift response. (C) 2000 Academic P ress.