Abstract
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.
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Luongo, A., Paolone, A. Perturbation Methods for Bifurcation Analysis from Multiple Nonresonant Complex Eigenvalues. Nonlinear Dynamics 14, 193–210 (1997). https://doi.org/10.1023/A:1008201828000
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DOI: https://doi.org/10.1023/A:1008201828000