Degenerate bifurcation analysis on a parametrically and externally excitedmechanical system

A general parametrically and externally excited mechanical system is consid ered. The main attention is focused on the dynamical properties of local bi furcations as well as global bifurcations including homoclinic and heterocl inic bifurcations. In particular, degenerate bifurcations of codimension 3 are studied in detail. The original mechanical system is first transformed to averaged equations using the method of multiple scales. With the aid of normal form theory, the explicit expressions of the normal form associated with a double-zero eigenvalue and Z(2)-symmetry for the averaged equations are obtained. Based on the normal form, it has been shown that a parametric ally and externally excited mechanical system can exhibit homoclinic and he teroclinic bifurcations, multiple limit cycles, and jumping phenomena in am plitude modulated oscillations. Numerical simulations are also given to ver ify the good analytical predictions.