Solution Diagram Of Non-Linear Dynamic Systems By The IHB Method

Abstract It is well known that a number of solutions may coexist in non-linear systems. Therefore, a complete solution diagram is very important in solving non-linear vibration problems in order to ensure that all possible solutions have been sought. This paper is aimed at seeking solution diagrams by means of performing parametric studies. In particular, the Incremental Harmonic Balance (IHB) method is used in the study. By introducing a parameter, this method can give solution diagrams of different non-linear dynamic systems, even with strong non-linearity. Examples of van der Pol oscillators and coupled oscillators are used to illustrate the effectiveness of the method and the importance of obtaining solution diagrams. Hopf bifurcations will also be discussed with these solution diagrams.