On the convergence of the Volterra-series representation of the Duffingʹs oscillators subjected to harmonic excitations

This paper is concerned with the investigation of the convergence issue of the Volterra-series representations of the Duffingʹs oscillator subjected to harmonic inputs. A simple criterion is proposed to determine the upper limit of the magnitude of the harmonic inputs. A comparison between the new proposed criterion and a criterion suggested by Tomlinson et al. [G.R. Tomlinson, G Manson, G.M. Lee, A simple criterion for establishing an upper limit to the harmonic excitation level of the Duffing oscillator using the Volterra series. Journal of Sound and Vibration 190 (1996) 751–762] was carried out. The results show that the new criterion can provide a more accurate prediction about the convergence of the Volterra-series representation of the Duffingʹs oscillator.