NONLINEAR-INTERACTIONS IN A PARAMETRICALLY EXCITED SYSTEM WITH WIDELYSPACED FREQUENCIES

An investigation is presented into the transfer of energy from high- t o low-frequency modes. The method of averaging is used to analyze the response of a two-degree-of-freedom system with widely spaced frequenc ies and cubic nonlinearities to a principal parametric resonance of th e high-frequency mode. The conditions under which energy can be transf erred from high- to low-frequency modes, as observed in the experiment s, are determined. The interactions between the widely separated modes result in various bifurcations, the coexistence of multiple attractor s, and chaotic attractors. The results show that damping may be destab ilizing. The analytical results are validated by numerically solving t he original system.