GLOBAL BIFURCATIONS IN EXTERNALLY EXCITED 2-DEGREE-OF-FREEDOM NONLINEAR-SYSTEMS

In this study we examine the global dynamics associated with a generic two-degree-of-freedom (2-DOF), coupled nonlinear system that is exter nally excited. The method of averaging is used to obtain the second or der approximation of the response of the system in the presence of one -one internal resonance and subharmonic external resonance. This syste m can describe a variety of physical phenomena such as the motion of a n initially deflected shallow arch, pitching vibrations in a nonlinear vibration absorber, nonlinear response of suspended cables etc. Using a perturbation method developed by Kovacic and Wiggins (1992), we sho w the existence of Silnikov type homoclinic orbits which may lead to c haotic behavior in this system. Here two different cases are examined and conditions are obtained for the existence of Silnikov type chaos.