A Digital Method of Evaluating Nonlinear Frequency Response Functions Based on Conditioned Spectral Analyses

Abstract This paper focuses on the issue of evaluating nonlinear frequency response functions (NOFRFs) of the nonlinear systems with a general input. A new digital approach of evaluating NOFRFs is proposed based on the method of conditioned spectral analysis (CSA). Firstly, a multiple-input/single-output (MISO) linear system with a series of power characterized inputs is obtained by decomposing a nonlinear system according to the NOFRFs theory. Secondly, the correlations among the inputs of various orders are removed by applying CSA method, obtaining an algorithm of identifying the NOFRFs and evaluating the contributions of different order nonlinearities to the output of the system. In the CSA procedure, the different order inputs are conditioned in the sequence from the first order to the highest order. Lastly, two kinds of nonlinear systems with a general input are simulated to verify the effectiveness of the proposed approach on evaluating the frequency response properties of nonlinear systems. It is shown that the results reached by the proposed method are very close to the numerical results obtained by the fourth order Runge-Kutta method, verifying that the proposed method is very effective on the evaluation of NOFRFs.