THE KRYLOV-BOGOLIUBOV AND GALERKIN METHODS FOR NON-LINEAR OSCILLATIONS

✍ Scribed by P. Yu; Y.M. Desai; N. Popplewell; A.H. Shah

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 663 KB
• Volume: 192
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1996.0195

✦ Synopsis

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.