Abstract:
The dynamic behavior of the Duffing-van der Pol oscillator with fractional-order derivative and parametric excitation is studied in this paper. The effects of various parameters on the amplitude-frequency curves of the system under the combined action of viscous inertia (1≤
p≤2) and parametric excitation are analyzed. The system is analyzed by the averaging method, and the fractional-order derivative is treated by the concepts of equivalent linear damping and equivalent mass. The approximate analytical solution of the system is obtained and compared with the numerical solution. The curves of the two solutions agree well with each other to a large extent, which proves the correctness of the analytical solution. The influences of system parameters on the amplitude-frequency curve are analyzed. It is found that the resonance peak value, resonance frequency, resonance region, the range and the number of multivalued solutions are all affected by the system parameters. Through analysis, it is found that the external excitation amplitude and the coefficient of fractional-order derivative can suppress the effect of parametric excitation to some extent.