Identification and parameter estimation of cubic nonlinear damping using harmonic probing and volterra series

摘要

Dynamic systems, such as vibration isolators, rotor-bearing systems, are inherently nonlinear and their dynamic behaviour often cannot be sufficiently explained or predicted by simple linear models. Presence of nonlinearity leads to certain characteristic behaviours in the response such as jump phenomenon, limit cycle, superharmonic resonances and such behaviours can be accurately predicted only if the nonlinearity structure and related parameters are properly known. This emphasises the recently growing importance of nonlinear system identification. A majority of the identification works is based on a-priori knowledge of nonlinearity structure and most of them consider only stiffness nonlinearities, such as Duffing's oscillator and bilinear oscillator. Not much work has been reported on nonlinearity structure identification for systems with damping nonlinearities. This paper, first discusses a systematic classification of nonlinearity structures based on first, second and third harmonic response amplitudes under harmonic excitation. Characteristics response for individual nonlinearity class is explained by Volterra series response formulation with higher order Frequency Response Functions. In the second part, a typical cubic damping nonlinearity is identified from cubic stiffness nonlinearity and an algorithm for estimating the nonlinear and linear damping parameters is developed. A new term called measurability ratio is introduced to show how it can help in deciding the most appropriate excitation frequency. Effect of truncating the Volterra series response on parameter estimation error is also studied for different excitation frequencies and varying excitation levels. It is shown that, with recursive iteration in computation of third harmonic amplitude, estimation accuracy can be further improved.