Resonance Analysisfor Weakly Nonlinear Duffing-van der Pol Oscillation

The resonance phenomena of a weakly nonlinear, damped, Duffing-van der Pol oscillation is studied analytically and numerically. The methods of multiple scales is used to obtain uniformly valid asymptotic approximate solutions of the governing equation for various cases of primary harmonic resonance, super-harmonic resonance and sub-harmonic resonance respectively. The study shows that the steady amplitudes in the solutions of the nonlinear equation demonstrate the nonlinear phenomena involving jump and bistability at some bifurcation points. The quantitative relations of Frequency-Amplitude involving the parameters of damping, nonlinear, external force in the oscillator are obtained. The asymptotic approximation and numerical solutions are in vertically perfect agreement for all the cases considered. The results enrich previous researches just for Duffing or van der Pol oscillation respectively. © 2024, International Association of Engineers. All rights reserved.