Nonlinear Modal Analysis Based on Nonlinear Output Frequency Response Functions (NOFRFs)

Abstract Nonlinear Output Frequency Response Functions (NOFRFs), as an extension of the linear Frequency Response Function (FRF) to nonlinear cases, were originally introduced for the investigation of nonlinear dynamics, and recently have been extensively used for system identification and structural health monitoring. However, the traditional NOFRFs are only valid to the nonlinear frequency analysis of single input and single output systems and cannot be generalized to multiple inputs multiple outputs systems. In this paper, the Generalized Associated Linear Equations (GALEs) in single-input and single-output systems are briefly introduced and then extended to multiple inputs multiple outputs nonlinear systems, with a method for calculating the NOFRFs matrix in multiple inputs multiple outputs systems proposed. Furthermore, based on the identified NOFRFs matrix, a new Nonlinear Modal Analysis, built on the NOFRFS is, for the first time, proposed for nonlinear multi degree of freedom systems. A numerical case study on two-degree-of-freedom system demonstrates the feasibility and validity of the proposed NOFRF-NMA.