Avoidance of artifacts in harmonic balance solutions for nonlinear dynamical systems

Abstract

Although nonlinear mechanical systems have been the topic of numerous investigations during the last decades, the research on suitable analysis methods is still ongoing. One method that is commonly known and still sees a lot of interest is the Harmonic Balance method. In the basic version of this method, only one harmonic is used to approximate a periodic solution, which allows for fairly easy application. A drawback is that this approach may lead to solutions that are inaccurate or even artifacts which are solutions that possess no physical relevance. In this article, it is demonstrated how an error criterion can be used to access the accuraccy of solutions and how artifacts can be indentified based on this assessment. Subsequently, stability analysis is performed for solutions that possess small errors. The method is applied to an asymmetric Duffing oscillator as well as to a system that consists of two linearly coupled Duffing oscillators. The authors gave a corresponding presentation of their work at PCM-CCM Kraków 2019.