Multiple Scale Analysis for Divergence-Hopf Bifurcation of Imperfect Symmetric Systems

The multiple time-scale method is adapted to study the post-critical behavior of general non-conservative symmetric systems, possibly affected by imperfections, for which divergence and Hopf bifurcations interact. The procedure illustrated makes it possible to elude the computational burden related to the application of the center manifold reduction. It also furnishes explicit expressions of the coefficients of the standard normal form bifurcation equations in terms of the coefficients of the original system. As an example, the method is applied to a two-degree-of-freedom rigid bar subjected to axial load (Augusti’s model) and transversal flow. The critical and post-critical scenarios are analyzed in detail, for both the perfect and imperfect systems.