Equivalent research on random vibration of strong nonlinear Duffing system;

It confirms that the faint characteristics signal impacts Duffing system much larger than others.

Taking the superposition principle as a criterion and calculating dynamic response of Duffing-type sliding systems to double-frequency harmonic excitations,the vibration nonlinearity of systems and their influence factors are analyzed.

Application of Duffing System in Detecting Faint Characteristics Signal Of Structural Damage

Super-harmonic resonance of Duffing-van der Pol system to multi-frequency excitation;

Methods of random Melnikov process function are introduced to analyze the equation and the differential trajectory,the influence of non-Gaussian color noise on Duffing oscillator chaotic motion behavior is also studied,a new chaotic method for the sine wave parameter estimation in non-Gaussian color noise environment is given.

Duffing oscillators’ phase transformation from chaos to intermittent chaos is sensitive to the signals, whose frequency difference is little different from the reference signal, while it has immune to white noise and the signals, whose frequency is quite different from the reference signal.

This article,through studying bifurcation and singularity of Duffing equation,by making use of the characteristics that Duffing oscillators produce spectrum approximates to white noise after enough bifurcation under perturbation of weak sinusoidal signal,analyzes bifurcation equation of Duffing oscillators and spectrum features.