Piecewise Volterra modeling of the Duffing oscillator in the frequency-domain

Abstract

When analyzing the nonlinear Duffing oscillator, the weak nonlinearity is basically dependent on the amplitude range of the input excitation. The nonlinear differential equation models of such nonlinear oscillators, which can be transformed into the frequency domain, can generally only provide Volterra modeling and analysis in the frequency-domain over a fraction of the entire framework of weak nonlinearity. When the amplitude of the excitation exceeds a certain value, the underlying nonlinear differential equation will become invalid in the frequency domain. This paper discusses the problem of using a new non-parametric routine to extend the capability of Volterra analysis, in the frequency domain, to weakly nonlinear Duffing systems at a much wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address.