Perturbation methods for bifurcation analysis from multiple nonresonant complex eigenvalues

Angelo Luongo (1) , Achille Paolone (2)

1 DICEAA - Dipartimento di Ingegneria Civile, Edile-Architettura, Ambientale
2 DISG - Dipartimento di Ingegneria Strutturale e Geotecnica

It is shown that the logical bases of the static perturbation method, which is currently used in static bifurcation analysis, can also be applied to dynamic bifurcations. A two-time version of the Lindstedt-Poincaré Method and the Multiple Scale Method are employed to analyze a bifurcation problem of codimension two. It is found that the Multiple Scale Method furnishes, in a straightforward way, amplitude modulation equations equal to normal form equations available in literature. With a remarkable computational improvement, the description of the central manifold is avoided. The Lindstedt-Poincaré Method can also be employed if only steady-state solutions have to be determined. An application is illustrated for a mechanical system subjected to aerodynamic excitation.

Domaines: Autre

Angelo Luongo, Achille Paolone. Perturbation methods for bifurcation analysis from multiple nonresonant complex eigenvalues. Nonlinear Dynamics, 1997, 14 (3), pp.193-210. ⟨hal-00799048⟩