The Krylov-Bogoliubov and galerkin methods for non-linear oscillations

The objective of this paper is to consider the dynamic motions of second order, weakly non-linear, discrete systems. The main attention is focused on a comparison, for such systems, of the method of Krylov-Bogoliubov (KB) and an enhanced Galerkin (EG) method which produce seemingly different solutions. Despite the apparent differences, the two methods are shown to give identical first order periodic and quasi-periodic solutions, and the same stability conditions for internal and external resonances, as well as a non-resonance. The ease of applying one or the other method depends upon whether a system is resonant and upon the number of participating modes. Both approaches are used here to analyze illustrative examples that are pertinent to galloping. (C) 1996 Academic Press Limited