A method of non-linear modal identification from frequency response tests

Abstract

A theoretical and experimental study of non-linear systems governed by Duffing's equation is presented in this study. The non-linear mode concept is applied to analyze the steady state responses of non-linear systems driven by a harmonic force. In the experimental context, the present modal identification method permits one to obtain the non-linear modal parameters from frequency response tests. By comparison with other methods, the proposed methods appear very interesting in regard to computational time, formulation, and they necessitate fewer computer resources. An experimental work on the steady state response of a beam with local non-linear stiffness is reported to justify the methods. Many aspects of theoretical results, such as the dependence of resonance frequency on the amplitude of vibration and the downward and upward jump phenomena are observed experimentally. The experimental results are in good agreement with theoretical predictions based upon the non-linear modal superposition approach.