Phase Quadrature Backbone Curve for Nonlinear Modal Analysis of Nonconservative Systems

Abstract

Nonlinear normal modes (NNMs) are often used to predict the backbone of resonance peaks in nonlinear frequency response functions. Regardless of the definition considered, one important limitation remains, i.e., the NNMs require a multi-point, multi-harmonic external forcing to be excited. To address this limitation, the present study proposes a new definition of NNMs, termed phase quadrature backbone curve (PQBC). The advantage of PQBC is that an actual solution of the nonlinear frequency response obtained under mono-point, mono-harmonic external forcing is followed for which phase quadrature of a selected degree of freedom is achieved. Additionally, super and subharmonic resonance peaks can be captured by adapting the phase quadrature condition. Finally, no post-processing is required to get amplitude-forcing relations of the NNMs. Isolated responses can, in turn, be predicted from these relations.