Influence of Nonlinear Distortions on Frequency Responses of a Hardening Duffing Oscillator with Linear Viscous Damping

In the present study, influence of the nonlinear distortions of the frequency response estimators of a Duffing system with a linear viscous damping and a cubic stiffness nonlinearity is investigated. Time domain responses are computed at four rms levels of random force excitation and the frequency response functions, H۱ and H۲ estimators are calculated using Welch's method. Also, the raw estimates, not smoothed and averaged FRFs, are used to illustrate the random error which is mainly caused by nonlinear distortions. The trends of the resonant and super-harmonic resonant bandwidths are studied and the identified damping factors are analyzed for H۱ and H۲ estimators. Theresults show that although the damping is linear and thus, independent of the force level, the resonant bandwidth widens due to the influence of cubic stiffness nonlinearity. Widening of the resonant bandwidth leads to a systematic error in damping identification, which increases with the excitation level.

کلیدواژه ها:

frequency response function ، random error ، Welch's method ، Duffing equation ، cubic stiffness ، damping identification ، resonant bandwidth ، multi-sine