A unified perturbation approach to static/dynamic coupled instabilities of nonlinear structures

A unified perturbation approach, based on the multiple scale method, able to analyse interactions among static and/or dynamic bifurcations of nonlinear structures, is illustrated. The method appears as the natural extension to the dynamical case of the static perturbation method, well-known in buckling of elastic structures. To illustrate the algorithm, a general, multiparameter, finite-dimensional autonomous system is considered, simultaneously undergoing a static (divergence) and two dynamic (Hopf) bifurcations, of nonresonant or resonant type. The method furnishes bifurcation equations governing the time-evolution of amplitudes and phases of the critical interacting modes. Results relevant to sample structures are discussed.