ON THE APPLICATION OF IHB TECHNIQUE TO THE ANALYSIS OF NON-LINEAR OSCILLATIONS AND BIFURCATIONS

Abstract

The main objective of this paper is to introduce certain refinements and alternative formulations, which enhance the applicability and availability of the intrinsic harmonic balancing technique. This is achieved by considering certain illustrative examples concerning non-linear oscillations and dynamic bifurcation phenomena. Indeed, the bifurcation behaviour of a harmonically excited non-autonomous system is analyzed conveniently, with reference to the corresponding autonomous system, by applying the IHB technique, which yields the bifurcation equation as an integral part of the perturbation procedure. A symbolic computer language, namely MAPLE, facilitates the analysis as well as verification of the ordered approximations to the solutions. The methodology lends itself to MAPLE readily, which in turn, enhances the applicability of the IHB technique.