Analysis of output response of nonlinear systems using nonlinear output frequency response functions

In the present study, the relationship between the Harmonic Balance Method (HBM) and the Nonlinear Output Frequency Response Functions (NOFRFs) approach when analysing the output response of nonlinear systems is investigated, showing that the output response described by the NOFRFs is the minimum solution of that from the HBM. After that, the convergent range of the NOFRFs is determined based on the proposed relationship, indicating that, outside this range, the validity of the NOFRFs method should be taken into account when used to represent the output response of nonlinear systems. Moreover, the effect of system damping on the convergence of the NOFRF approach is studied. The results imply that a nonlinear system with appropriate linear or nonlinear damping may have no convergence issue when being analysed using a NOFRFs-based method.