Efficient energy balancing across multiple harmonics of nonlinear normal modes

Abstract Predicting the forced responses of nonlinear systems is a topic that attracts extensive studies. The energy balancing method considers net transfer in and out system over one period establishes connections between normal modes (NNMs). In this paper, we consider across multiple harmonics NNMs for predicting resonances. This technique constructed by combining mechanism with restrictions (established via excitation scenarios) on external forcing harmonic phase-shifts; semi-analytical framework derived to achieve both accurate/robust results efficient computations. With known inputs from NNM solutions, required amplitudes reach at resonances, along their discrepancy, i.e. phase-shifts, are computed one-step scheme. Several examples presented different scenarios demonstrate applicability show its capability accurately existence an isola where play significant part response.