Position and velocity time delay for suppression vibrations of a hybrid rayleigh-van der pol-duffing oscillator

Abstract

In this paper, we used time delay feedback to minimize the vibrations of a hybrid Rayleigh-van der Pol-Duffing oscillator. This system is a one-degree-of-freedom containing the cubic and fifth nonlinear terms and an external force. We applied the multiple scales method to get the solution from first approximation. Graphically and numerically, we studied the system before and after adding time delay feedback at the primary resonance case ( ffi !). We used MATLAB program to simulate the efficacy of different parameters and the time delay on the main system.