Controlling the Primary Resonance Vibrations of a Hybrid Rayleigh-Van der Pol-Duffing Oscillator Using Negative Cubic Velocity Feedback

Abstract

This study aims to suppress vibrations in hybrid Rayleigh-Van der Pol-Duffing oscillators by employing negative cubic velocity feedback control. The system's behavior is analyzed using the multiple-scales method to derive solutions up to the second-order approximation. The effect of negative cubic velocity feedback is specifically examined under primary resonance conditions. The influence of various system parameters is explored numerically using MATLAB. The findings reveal a strong correlation between the approximate analytical solutions and numerical results, confirming the effectiveness of the proposed approach.