Comparison of different harmonic balance based methodologies for computation of nonlinear modes of non-conservative mechanical systems

For the determination of periodic solutions for forced or free vibrations of nonlinear systems, several proven methods exist. The motion of autonomous nonlinear non conservative mechanical systems is in general non-periodic which contradicts the computation of their nonlinear modes as natural periodic solutions. Utilizing the harmonic balance method (HBM) two approaches for nonlinear mode computation of non conservative systems exist - the so called concept of complex nonlinear modes (CNM) and the extension of the periodic motion concept (E-PMC). Each nonlinear mode computed using one of these methods is then described by its frequency, damping, the harmonics, and the corresponding phase angles of each degree of freedom as functions of the generalized amplitude. Applying averaging methods transient system responses of the system can be efficiently computed regarding one nonlinear mode. In this work differences between complex nonlinear modes and the extended periodic motion concept as well as corresponding results will be addressed. (C) 2019 Elsevier Ltd. All rights reserved.