A Waveform Similarity Approach for Diagnosing Nonlinear Behavior of Vibratory Systems

Abstract

A new approach is proposed for diagnosing the nonlinear characteristics of vibratory systems in engineering applications. The correlation coefficient of two periods’ response wave is used in this approach and a new concept named similarity degree of waveform (SDW) is proposed to describe the correlations of the responses and therefore the characteristics of the nonlinear dynamic systems. A Duffing system is used in this research as an example to demonstrate the application and efficiency of the proposed approach. The approach has shown effectiveness in diagnosing periodic, multi-periodic, quasi-periodic and chaotic motions. The characterization with implementing the proposed approach is compared with that of the Lyapunov exponent method. The advantages of the proposed approach are demonstrated.